Gray Code

Genetic algorithms have been extensively used and studied in computer science, yet there is no generally accepted methodology for exploring which parameters significantly affect performance, whether there is any interaction between parameters, and how performance varies with respect to changes in parameters. This paper presents a rigorous yet practical statistical methodology for the exploratory study of genetic and other adaptive algorithms. This methodology addresses the issues of experimental design, blocking, power calculations, and response curve analysis. It details how statistical analysis may assist the investigator along the exploratory pathway. As a demonstration of our methodology, we describe case studies using four well-known test functions. We find that the effect upon performance of crossover is predominantly linear, while the effect of mutation is predominantly quadratic. Higher order effects are noted but contribute less to overall behavior. In the case of crossover, both positive and negative gradients are found suggesting the use of a maximum crossover rate for some problems and its exclusion for others. For mutation, optimal rates appear higher compared with earlier recommendations in the literature, while supporting more recent work. The significance of interaction and the best values for crossover and mutation are problem specific.

J matrix whose entries are all zero. I, and J, are the N x N identity and opposite identity matrices, respectively. 1', denotes an N x N diagonal matrix defined as Ih = diag[fi, 1, ..., 1 1 Proposed cosine-modulated FIR filter banks: To describe the proposed CMFBs with 2N sub-channels, two cases for N, odd or even, are considered separately. We also assume that the length of the prototype filter h(n) is L = 2NM, and the type 1 polyphase components of H(z) are H,(z) (q = 0, 1, ..., 2N-I). The CMFBs are defined as (i) for N even (N = 2m) Uk(?2) = g h (n) c o s (" " y y)) k = 0,1,. .. j N-1

This paper presents three multimedia encryption algorithms base on a new Generalized P-Gray Code (GPGC) to protect the surveillance data in homeland security applications. The GPGC is a k-digital parametric sequence suitable for any base, n. It is also called the (n, k, p)-Gray Code where p is a parameter that allows the users to change the distance to yield different Gray Code sequences. The base n and parameter p as security keys have many options to make the encrypted multimedia difficult to decode. This allows the encrypted objects to be protected with high levels of security. The experimental results verify that the presented algorithms are lossless approaches and good at partial multimedia encryption. A method of measuring the percentage of image encryption is introduced and the measure results are also provided to quantify the encryption performance. Experiments demonstrate that the algorithms show good performance for the common attacks. Due to the low complexity of the algorithms, they are also suitable for real-time applications. The principles behind the presented solutions may be applied to various image, audio, and video systems.

An efficient algorithm searching for the best (shortened) cyclic burst-correcting codes is presented. The efficiency of the algorithm stems from the fact that no repeated syndromes are computed. It is shown how to achieve this goal by using Gray codes.

This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation cost of symmetric functions based on these expressions by exploiting Gray decoding of input variables. Although this decoding is a particular example of all possible linear transformation of Boolean variables, it is efficient in the case of symmetric functions since it provides a significant simplification of SOPs and FPRMs. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.

A parity generator is a circuit that generates redundant bits used for error detection and is used when transmitting binary information. Previous parity generator circuits based on quantum-dot cellular automata (QCA) are designed to reduce the area of the circuit. Input cells of existing circuit are designed inside the circuit and the circuit’s signal is not propagated properly due to the influence between adjacent wires. In addition, existing circuits consume many clocks because the XOR gate, which is an essential component of the parity generator circuit, consumes many clocks. In order to solve this problem, we design a 3-bit odd parity generator circuit using QCA for fast operation. The proposed circuit uses an XOR gate that can operate one clock faster than the existing XOR gate to reduce the clock, and by extending this XOR gate, the output value can be obtained faster than the conventional circuit. In the proposed circuit, the result is verified through simulation and the performance is compared with the existing circuit.

Let T(n) be the set of all well-formed parentheses strings of length 2n. We show that the elements of T(n) can be listed so that successive strings differ by the transposition of a left and a right parenthesis. Furthermore, between the two parentheses that are transposed, only left parentheses occur. Our listing is a modification of the well-known Eades-McKay (1984) algorithm for generating combinations. Like that algorithm, ours generates strings from the lexicographically greatest string to the lexicographically least and can be implemented so that each string is generated in constant time, in an amortized sense.

and link-faults in a hypercube multipro-;.,*,..r. tt'i reuealed lhal, the direct use of sharp prod-.t:t opcration is not sufficient lo discard onlg compulrir-rnrr/ oarl (processor and mernory), when onlg this ;tt1 ,:i node is faulty. We also showed lhal in case 'z ta some links in comrnunicalion part (router) in-*i,tn! lo a healthy node are faulty, the sharp product 6tmlton does not altow to leaue the healthy links and :i; rode tncident to lhese links in the set of healthy ,tkr0es. In order to remoue tltis defficiencg, we prov:tr. forma! procedures with aid of which we can subrr:ri yirsl only the faultg node, ercluding the healthy rats tncidenl to this node and second onlg the faultg tak. etcluding also the healthE nodes incident lo these lats. The procedures are independent from tlte nurnkr and scaltering of faultg elernents in hEpercube. li'x. the proposed procedures allow to obtazn a sel { criend.ed fault-free subcubes, that is a beginning sel hr further manipulation in hgpercabe rnultiproce$sors tai Lncrease the reliability of such sgstems.

Genetic algorithms have been extensively used and studied in computer science, yet there is no generally accepted methodology for exploring which parameters significantly affect performance, whether there is any interaction between parameters, and how performance varies with respect to changes in parameters. This paper presents a rigorous yet practical statistical methodology for the exploratory study of genetic and other adaptive algorithms. This methodology addresses the issues of experimental design, blocking, power calculations, and response curve analysis. It details how statistical analysis may assist the investigator along the exploratory pathway. As a demonstration of our methodology, we describe case studies using four well-known test functions. We find that the effect upon performance of crossover is predominantly linear, while the effect of mutation is predominantly quadratic. Higher order effects are noted but contribute less to overall behavior. In the case of crossover, both positive and negative gradients are found suggesting the use of a maximum crossover rate for some problems and its exclusion for others. For mutation, optimal rates appear higher compared with earlier recommendations in the literature, while supporting more recent work. The significance of interaction and the best values for crossover and mutation are problem specific.

This paper discusses the trade-off between accuracy, reliability and computing time in the binary-encoded genetic algorithm (GA) used for global optimization over continuous variables. An experimental study is performed on a large set of analytical test functions. We show ®rst the limitations of the ªstandard GAº, which mostly requires a high computing time, though exhibiting a low success rate, due to premature convergence. We then point out the disappointing effect of carefully choosing and tuning the ªclassicalº GA parameters, such as the code and mutation or crossover operators. Indeed, Gray coding and double crossover helped improving on speed, but did not answer the problem of a too homogeneous population. To ®ght the premature convergence of GA, we emphasize at last two deciding alterations made to the algorithm: an adaptive reduction of the de®nition interval of each variable and the use of a scale factor in the calculation of the crossover probabilities. The enhanced GA so achieved is discussed in detail and intensively tested on more than 20 test functions of 1±20 variables.

Both Gray code and binary code are frequently used in mapping arrays into hypercube architectures. While the former is preferred when communication between adjacent array elements is needed, the latter is preferred for FFT-type communication. When di erent phases of computations have di erent types of communication patterns, the need arises to remap the data. We give a nearly optimal algorithm for permuting data from a Gray code mapping to a binary code mapping on a hypercube with communication restricted to one input and one output channel per node at a time. Our algorithm improves over the best previously known algorithm 6] by nearly a factor of two and is optimal to within a factor of n=(n 1) with respect to data transfer time on an n-cube. The expected speedup is con rmed by measurements on an Intel iPSC/2 hypercube.

We compare term by term the paperfolding sequence with a copy displaced by d terms to obtain the matching fraction M (d). It is shown that M (d) has an interesting structure in that if d = 2 b (1+2s), then M (d) = 1 − 3 2 b+1 thereby generating horizontal bands for each value of b. That is, M (d) depends only on b.

Three equivalent methods of generating the paperfolding sequence are presented as well as a categorisation of runs of identical terms. We find all repeated subsequences, the largest repeated subsequences and the spacing of singles, doubles and triples throughout the sequence. The paperfolding sequence is shown to have links to the Binary Reflected Gray Code and the Stern-Brocot tree.

In this paper we address visual communications via printing channels from an information-theoretic point of view as communications with side information. The solution to this problem addresses important aspects of multimedia data processing, security and management, since printed documents are still the most common form of visual information representation. Two practical approaches to side information communications for printed documents are analyzed in the paper. The first approach represents a layered joint source-channel coding for printed documents. This approach is based on a self-embedding concept where information is first encoded assuming a Wyner-Ziv set-up and then embedded into the original data using a Gel'fand-Pinsker construction and taking into account properties of printing channels. The second approach is based on Wyner-Ziv and Berger-Flynn-Gray set-ups and assumes two separated communications channels where an appropriate distributed coding should be elaborated. The first printing channel is considered to be a direct visual channel for images ("analog" channel with degradations). The second "digital channel" with constrained capacity is considered to be an appropriate auxiliary channel. We demonstrate both theoretically and practically how one can benefit from this sort of "distributed paper communications".

In this paper we address visual communications via print-and-scan channels from an information-theoretic point of view as communications with side information that targets quality enhancement of visual data at the output of this type of channels. The solution to this problem addresses important aspects of multimedia data processing and management.

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Compatibility of a design is an archetype of three aspects, namely speed, power, and area. Achieving all three of them is exceptionally desirable. Quantum-dot Cellular Automata is one of the most surrogate nanotechnologies in the electronics industry. Being a low power utilizer, a high-speed operator, and Nano-size when it comes to the fabrication process, it has its own leverages. Quantum-dot Cellular Automata cells are assimilated in wires and logic gates as a fundamental building block of nanoscale digital circuits. Implementing QCA circuits with the help of the XOR gate, the circuit can be made simpler in delay and cell count. One of the sequential circuits, a flip-flop is a circuit which stores and controls data. This paper presents a compact negative-edge triggered T flip-flop structure in a superlative form. The T in T flip-flop is stands for "toggle" which is a circuit used for counter configuration. Depending on the clock signal, they are grouped into falling-edge triggered and rising-edge triggered flip-flops. When the clock rises or falls, the state of the output value changes. The T flip-flop design is focused to reduce cell count, area consumption and energy dissipation as compared to earlier and existing designs.

A parity generator is a circuit that generates redundant bits used for error detection and is used when transmitting binary information. Previous parity generator circuits based on quantum-dot cellular automata (QCA) are designed to reduce the area of the circuit. Input cells of existing circuit are designed inside the circuit and the circuit's signal is not propagated properly due to the influence between adjacent wires. In addition, existing circuits consume many clocks because the XOR gate, which is an essential component of the parity generator circuit, consumes many clocks. In order to solve this problem, we design a 3-bit odd parity generator circuit using QCA for fast operation. The proposed circuit uses an XOR gate that can operate one clock faster than the existing XOR gate to reduce the clock, and by extending this XOR gate, the output value can be obtained faster than the conventional circuit. In the proposed circuit, the result is verified through simulation and the performance is compared with the existing circuit.

Quantum dot cellular automata (QCA) is growing technology with Nano range scale in that, QCA is extremely computational and exceptionally productive than CMOS technology. QCA the parameters like area and usage of power are very less when compared to CMOS technology. In the comparative analysis of QCA and CMOS technologies, the number of quantum cells used and the number of transistors taken place to design 3 input logic gates. In this paper, it explains about the comparison between CMOS and QCA technologies for 3 input basic logic gates like AND, OR, NOT, NAND, NOR ,XOR and XNOR by utilizing the ultra-low power and the area, time taken to outline the circuit with quantum dot cells in QCA technology. From the results, area utilized to design logic gates using by QCA technology as compared to CMOS technology is reduced up to 5%.

Quantum-dot Cellular Automata (QCA) is an alternative innovation to the
Complementary Metal Oxide Semiconductor (CMOS) because CMOS has scaling
limitations that lead to high leakage power. QCA is structured on quantum cells, whose
sizes are on the nanoscale. This component causes faults in QCA circuits. Converting
a code into another that is programmed in logic arrays becomes important in the
physical realization of the circuits. There are many methods to resolve this problem in
circuits. A code converter is a solution to convert one code into another. In this paper,
QCA-based “4-bit binary-to-gray” and “4-bit gray-to-binary code converters” are
suggested. The offered layout prospects to a decrease in energy expenditure and can
be utilized in many fields for shielding data from outsiders and increasing information
flexibility. We executed a relative analysis of the suggested design with present earlier
designs and turned out that the suggested layout is productive on condition that
complexity, cell count, area intake, and clocking. This paper offers a streamlined design
and layout concerning code converters depending on QCA. These structures are
designed with the QCADesigner, simulator and the simulation results are examined

One of the important codes, a gray code is normally used to detect correction of error
in digital systems. Gray codes use a binary encoding scheme through grouping of the
order of the bits and changing one bit of the group. Quantum-dot cellular automata
(QCA) is a promising and a future technology for semiconductor transistor based
technologies. We propose an extendable QCA binary to gray code converter in this paper.
An Exclusive-OR gate is a core element in binary-to-code converter so we used an XOR
gate using Nand-Nor-Inverter (NNI) gate which can simplify to logic circuits. The NNI
gates are universal gates and can efficiently design XOR gates. A first proposed design is
a 2-bit circuit and we extend it to 3-bit and to 4-bit designs. The proposed circuits are
compared to previous designs and it shown its efficiency.Q

We consider the local rank-modulation scheme in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rankmodulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory.

Quantum-dot cellular automata is a promising nanotechnology and a possible alternative to complementary metal-oxide-semiconductor (CMOS) transistors. Nowadays, several sequential and combinational logic circuits have been designed and implemented using QCA nanotechnology. However the impact of energy dissipation constraint is still unobserved while the forming complex QCA circuits. This paper presents energy-efficient memory cell (JK flip-flop) and single layer counter circuit using QCA. Moreover, comprehensive energy consumption analysis of the proposed design along with structural comparison is performed over the state-of-the-art QCA memory cells. Experimental results show the computational supremacy of the proposed design in terms of cell counts, space intricacy, wire crossing and time delays. QCADesigner and QCAPro software tools are used for verifying the circuit functionality and estimating the energy dissipation of the proposed designs. Ó 2017 Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

In the present era, transistor reached their highest density and cannot go much smaller than their present size. There are many designs of QCA adders are present in literature, this is new multilayered schematic layout of adder based on QCA technology. In QCA main emphasis on the area and delay reduction leads to an efficient adder design. The proposed adder have less hardware complexity, such as number of cell , delay and total area .QCA designer is the software used form layout generation and simulation results are shown using the coherence vector engine in the same software. Keywords: full adder, quantum dot cellular automata, three inputs XOR (TIEO) Gate.

Quantum dot Cellular Automata (QCA) is a new direction in creating logic circuits based on
nanotechnology.It is a promising alternative to CMOS technology with many appealing features such as high speed,
lowpower consumption and higher switching frequency than transistor basedtechnology.The code converters are the
basic unit for alteringof datato perform arithmetic processes. In this paper, QCA based3-bit binary to gray and 4-bit
binary to gray code converter, with a minimum number of cells, has beenproposed.The simulations are completed using
QCA Designer.

In recent years Quantum-dot Cellular Automata (QCA) has been considered one of the emerging nano-technology for future generation digital circuits and systems. QCA technology is a promising alternative to Complementary Metal Oxide Semiconductor (CMOS) technology. Thus, QCA offers a novel electronics paradigm for information processing and communication system. It has attractive features such as faster speed, higher scale integration, higher switching frequency, smaller size and low power consumption compared to the transistor based technology. It is projected as a promising nanotechnology for future Integrated Circuits (ICs). A quantum dot cellular automaton complex gate is composed from simple 3-input majority gate. In this paper, a 8-3 encoder circuit is proposed based on QCA logic gates: the 4-input Majority Voter (MV) OR gate. This 7-input gate can be configured into many useful gate structures such as a 4-input AND gate, a 4-input OR gate, 2-input AND and 2-input OR gates, 2-input complex gates, multi-input complex gates. The proposed circuit has a promising future in the area of nano-computing information processing system and can be stimulated with higher digital applications in QCA.

The Tower of Hanoi Puzzle finds its applications ranging from robotics to psychological research. This puzzle is a classic case of recursive algorithm in programming. However, this puzzle can also be implemented using iterative programming, by using binary codes or gray codes. Various applications require an optimized solution for this puzzle. In this paper, an efficient implementation of Tower of Hanoi using Gray codes for 'n' disks and three rods is presented. This focuses only on minimizing storage and reducing running time as required by many applications. The proposed implementation using Gray code system consumes lesser memory and slightly reduced running time compared to the conventional recursive methodology.

A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been considered in the past, we provide a new, simple Gray code for fixed-weight m-ary strings. In addition, we consider a relatively new type of Gray code known as overlap cycles and prove basic existence results concerning overlap cycles for fixed-weight and weight-range m-ary words.

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is will known that Steiner quadruple systems of order v, or SQS(v), exist if and only if v ≡ 2, 4 (mod 6). Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole. Using Hanani's SQS constructions, we show that for every v ≡ 2, 4 (mod 6) with v > 4 there exists an SQS(v) that admits a 1-overlap cycle. * [email protected] † [email protected] Construction 2.2. Let (X, B) be an SQS with |X| = n. Let X = {0, 1, 2, . . . , n − 2} ∪ {A}. Let B = B A ∪ B A where B A denotes all blocks containing A and B A denotes all blocks not containing the point A. We construct new blocks on the set Y = ({0, 1, 2} × {0, 1, 2, . . . , n − 2}) ∪ {A}.

The basic theory of t-UEC (I-UED codes is developed. Methods for construction of such codes from symmetric error-correcting and asymmetric error-correcting codes are developed. Some bounds for t-EC (I-UED codes are improved. Encoding/decoding procedures for these codes are discussed.

Quantum-dot cellular automata (QCA) are a transistorless computation approach which encodes binary information via configuration of charges among quantum dots. The fundamental QCA logic primitives are majority and inverter gates which can be utilized to design various QCA circuits. This study presents a novel approach to designing efficient QCA-based circuits based on Boolean expressions achieved from reconfiguration of five-input and three-input majority gates. Whereas the multiplexer and Exclusive-or are the most important fundamental logical circuits in digital systems, designing efficient and single layer structures without coplanar cross-over wiring is advantageous in QCA technology. In order to demonstrate the efficiency and usefulness of the proposed approach, simple and dense multiplexer and Exclusive-or structures are implemented. The proposed designs have significant improvement in terms of area, complexity, latency, and gate count in comparison to previous designs. The correct logical functionalities of presented structures have been authenticated using QCA designer tool.

—Adiabatic logic brings about a great deal of power minimization in digital circuits. An application of the same is presented here by proposing a new design of some code converters-BCD to Excess-3, Binary to Gray and Gray to Binary, using the Adiabatic Array Logic. The proposed circuits show lesser power dissipation than the conventional static CMOS logic style and Two Phase Clocked Adiabatic Logic (2PASCL). The simulation is carried out in NI-Multisim software at 0.18m, 1.8V CMOS standard process technology over a frequency range of 200-800MHz.

We investigate the problem of listing combinations using a special class of operations, prefix shifts. Combinations are represented as bitstrings of 0's and 1's, and prefix shifts are the operations of rotating some prefix of a bitstring by one position to left or right. We give a negative answer to an open problem asked by F. , 570-576), that is whether we can generate combinations by only using three very basic prefix shifts on bitstrings, which are transposition of the first two bits and the rotation of the entire bitstring by one position in either direction (i.e., applying the permutations σ 2 , σ n and σ n −1 to the indices of the bitstrings).

Quantum dot Cellular Automata (QCA) is an emerging technology for development of logic circuits based on nanotechnology, and is one of the alternative for designing high performance computing over existing CMOS-VLSI technology. QCA does not use voltage level for logic representation rather it represents binary state by polarization of electrons in the QCA Cell. Conventional logic circuits are irreversible in nature and always lead to energy dissipation. Thus extensive research is going on to design the circuits which does not dissipation the energy and hence will not loose the information. In this paper we have designed the QCA based toffoli gate and then implemented the basic logic gates with it. The circuits were successfully simulated and verified by QCA Designer tool.

Quantum dot Cellular Automata (QCA) is an emerging technology for development of logic circuits based on nanotechnology, and is one of the alternative for designing high performance computing over existing CMOS-VLSI technology. QCA does not use voltage level for logic representation rather it represents binary state by polarization of electrons in the QCA Cell. Conventional logic circuits are irreversible in nature and always lead to energy dissipation. Thus extensive research is going on to design the circuits which does not dissipation the energy and hence will not loose the information. In this paper we have designed the QCA based toffoli gate and then implemented the basic logic gates with it. The circuits were successfully simulated and verified by QCA Designer tool.

Abstract Single-track Gray codes are cyclic Gray codes with codewords of length n, such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track. We investigate the structure of such binary codes and show that ...

Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code.

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. If no element of G moves any subset of Ω by more than m points (that is, |Γ g \ Γ| ≤ m for every Γ ⊆ Ω and g ∈ G), and also if each G-orbit has size greater than 7, then the number t of G-orbits in Ω is at most 1 6 (7m − 1). Moreover, the equality holds if and only if G is an elementary abelian 7-group.

Quantum-dot Cellular Automata (QCA) is a system with low power consumption and a potentially high density and regularity. Also, QCA supports the new devices with nanotechnology architecture. This technique works based on electron interactions inside quantum-dots leading to emergence of quantum features and decreasing the problem of future integrated circuits in terms of size. In this paper, we will successfully design, implement and simulate a new 2-input and 3-input XOR gate (exclusive OR gate) based on QCA with the minimum delay, area and complexities. Then, we will use XOR gates presented in this paper, in 2-bit, 4-bit and 8-bit controllable inverter in QCA. Being potentially pipeline, the QCA technology calculates with the maximum operating speed. We can use this controllable inverter in the n-bit adder/subtractor and reversible gate.

We present an analysis of the genotype-phenotype map in Grammatical Evolution (GE). The standard map adopted in GE is a depth-first expansion of the non-terminal symbols during the derivation sequence. Earlier studies have indicated that allowing the path of the expansion to be under the guidance of evolution as opposed to a deterministic process produced significant performance gains on all of the benchmark problems analysed. In this study we extend this analysis to include a breadth-first and random map, investigate additional benchmark problems, and take into consideration the implications of recent results on alternative grammar representations with this new evidence. We conclude that it is possible to improve the performance of grammar-based Genetic Programming by the manner in which a genotype-phenotype map is performed.

We present an analysis of the genotype-phenotype map in Grammatical Evolution (GE). The standard map adopted in GE is a depth-first expansion of the non-terminal symbols during the derivation sequence. Earlier studies have indicated that allowing the path of the expansion to be under the guidance of evolution as opposed to a deterministic process produced significant performance gains on all of the benchmark problems analysed. In this study we extend this analysis to include a breadth-first and random map, investigate additional benchmark problems, and take into consideration the implications of recent results on alternative grammar representations with this new evidence. We conclude that it is possible to improve the performance of grammar-based Genetic Programming by the manner in which a genotype-phenotype map is performed.

We present an analysis of the genotype-phenotype map in Grammatical Evolution (GE). The standard map adopted in GE is a depth-first expansion of the non-terminal symbols during the derivation sequence. Earlier studies have indicated that allowing the path of the expansion to be under the guidance of evolution as opposed to a deterministic process produced significant performance gains on all of the benchmark problems analysed. In this study we extend this analysis to include a breadth-first and random map, investigate additional benchmark problems, and take into consideration the implications of recent results on alternative grammar representations with this new evidence. We conclude that it is possible to improve the performance of grammar-based Genetic Programming by the manner in which a genotype-phenotype map is performed.

Covering, dominating, and induced paths in binary hypercubes are well-studied notions in combinatorics. For example, Blass et al. investigate lower bounds on the length of cube-dominating paths and cycles. In this talk, I will introduce a combinatorial problem of constructing lean induced cycles, which is defined to be longest chord-free cycles that span a minimum number of hypercube nodes. This problem is important in modeling gene networks in Systems Biology, as lean induced cycles correspond to stable network models. I will demonstrate how to use a SAT solver to compute lean induced cycles for hypercubes up to dimension 7 and classify the cycles with respect to the number of nodes they span. The classification is obtained using a custom-made All-SAT solver with blocking clauses. Efficient filtering of these clauses allows to reduce their number by two orders of magnitude for the 6-cube and thus to compute the classification in reasonable time.

We analyze the structure and enumerate Dumont permutations of the first and second kinds avoiding certain patterns or sets of patterns of length 3 and 4. Some cardinalities are given by Catalan numbers, powers of 2, little Schröder numbers, and other known or related sequences.

The term binary combinatorial Gray code refers to a list of
binary words such that the Hamming distance between two neighboring
words is one and the list satisfies some additional properties that are of interest
to a particular application, e.g., circuit testing, data compression, and
computational biology. New distance-preserving and circuit codes are presented
along with a complete list of equivalence classes of the coil-in-the-box
codes for codeword length 6 with respect to symmetry transformations of
hypercubes. A Gray-ordered code composed of all necklaces of the length
9 is presented, improving the known result with length 7.