Exhaustive Generation Research Articles

Using EPCG for Designing a Hexagon Tangram Puzzle

Designing and tuning a game is a complex creative process, with a variety of tools have been designed for assisting human designers in this process. But, many existing tools either entirely take the design away from humans, or they only assist in generating content - they cannot be used to create an entire game from scratch. This paper explores how Exhaustive Procedural Content Generation (EPCG) can be integrated as a co-creative partner in the design process. We describe how EPCG was used alongside human designers to create a novel Hexagon Tangram puzzle, from initial conception to puzzle curriculum. EPCG is used to answer design questions at each step of the design, which enable human designers to make more informed design choices.

Exhaustive Test Case Generation for Nuclear Safety Software Based on the Software Logic Model

An issue regarding the incorporation of software reliability within the nuclear power plant (NPP) probabilistic risk assessment model has emerged in the licensing processes of digitalized NPPs. Since software failure induces common-cause failure of the processor modules, the reliability of the software used in the NPP safety-critical instrumentation and control systems must be quantified and verified with proper test cases and environments. In this study, a software testing method based on the minimal cut set (MCS)–based exhaustive test case generation scheme is proposed where the software logic model is developed from available information on the software development and the MCSs that represent the necessary and sufficient conditions for the software variables’ states to produce safety software outputs are generated. The MCSs are then converted into the test cases, which can be used as inputs to the test bed to verify that the test cases produce correct outputs after software execution. The effectiveness of the proposed method is demonstrated with the safety-critical trip logic software of the APR-1400 reactor protection system. The method provides a systematic way to conduct exhaustive software testing and prove the functionality of the nuclear safety software based on the test result without uncertainties.

Universally Exhaustive Generation of Molecular Structures and Prediction of Their Electronic States Using Machine Learning for N-type Organic Transistor Materials.

We have proposed a new method for the exploration of organic functional molecules, using an exhaustive molecular generator combined without combinatorial explosion and electronic state predicted by machine learning and adapted for developing n-type organic semiconductor molecules for field-effect transistors. Our method first enumerates skeletal structures as much as possible and next generates fused ring structures using substitution operations for atomic nodes and bond edges. We have succeeded in generating more than 4.8 million molecules. We calculated the electron affinity (EA) of about 51 thousand molecules with DFT calculation and trained the graph neural networks to estimate EA values of generated molecules. Finally, we obtained the 727 thousand molecules as candidates that satisfy EA values over 3 eV. The number of these possible candidate molecules is far beyond what we have been able to propose based on our knowledge and experience in synthetic chemistry, indicating a wide diversity of organic molecules.

A machine learning framework for evaluating the biodiesel properties for accurate modeling of spray and combustion processes

The environment-friendly nature of biodiesel coupled with its inherent compression ignition fuel characteristics like better ignition quality, and fuel bound oxygen may reduce sooting combustion, and attract wide attention. The variation of thermophysical properties with temperature is essential for accurately modeling the combustion and emission characteristics of biodiesel fuelled diesel engines. Hence, the current paper attempts to predict the thermo-physical properties such as density, viscosity, specific heat, thermal conductivity, latent heat of vaporization, vapor pressure, mass diffusivity etc., and their variation with respect to the temperature following a machine learning approach for biodiesel fuels. Twenty feedstock samples are chosen for predicting the biodiesel thermo-physical properties and are validated with the available experimental data within a maximum error of 14 %. To evaluate the thermo-physical properties of a variety of feedstock, the predicted data are used for training an artificial neural network (ANN) and the developed ANN function is used for generating the various thermophysical properties of biodiesel fuels based on their composition and temperature. A good agreement is observed between the predicted and ANN results with a maximum mean absolute percentage error of 10 %. Hence in the current work, a collective mathematical modeling approach is proposed to accurately determine the spray and combustion-related fuel properties. The proposed model provides the various liquid and vapor properties and their variation with temperature which could be effectively employed for detailed spray and biodiesel-combustion modeling. An exhaustive data generation of eleven major liquid and vapour properties of twenty biodiesel fuels within the actual temperature range from 300 K to their respective critical temperature is presented.

On the exhaustive generation of discrete figures with connectivity constraints

Abstract This paper deals with a generalization of polyominoes called (a, b)-connected discrete figures, where a and b respectively denotes the connectivity of the foreground (i.e. black pixels) and background (i.e. white pixels). Formally, a finite set of pixels P is (a, b)-connected if P is a-connected and P̄ is b-connected. By adapting a combinatorial structure enumeration algorithm due to Martin, we successfully generate (a, b)-connected discrete figures up to size n = 18.

Curation of Computational Chemical Libraries Demonstrated with Alpha-Amino Acids.

Exhaustive generation of molecular structures has numerous chemical and biochemical applications such as drug design, molecular database construction, exploration of alternative biochemistries, and many more. Mathematically speaking, these are graph generators with chemical constraints. In the field, the most efficient generator currently (MOLGEN) is a commercial product, limiting its use. Alternative to that, another molecular structure generator, MAYGEN, is a recent open-source tool with efficiency comparable to MOLGEN and the capacity for users to increase its performance by adding new features. One of the research fields that can benefit from this development is astrobiology; structure generators allow researchers to supplement experimental data with computational possibilities for alternative biochemistry. This protocol details one use case for structure generation in astrobiology, namely the generation and curation of alpha-amino acid libraries. Using open-source structure generators and cheminformatics tools, the practices described here can be implemented beyond astrobiology for the low-cost creation and curation of chemical structure libraries for any research question.

On the generating functions of pattern-avoiding Motzkin paths

Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over x and the Catalan generating function C(x)=1−1−4x22x2, where x keeps track of the length of the path. Moreover, an algorithm is provided for finding the generating function in the more general case of an arbitrary set of patterns. In addition, this algorithm allows us to find a combinatorial specification for pattern-avoiding Motzkin paths, which can be used not only for enumeration, but also for exhaustive and random generation.

A Legendre pair of length 77 using complementary binary matrices with fixed marginals

We provide a search method for Legendre pairs of composite length based on generating binary matrices with fixed row and column sums from compressed, complementary integer vectors. This approach yielded the first construction of a Legendre pair of length 77, as well as the first exhaustive generation of Legendre pairs of length 55.

Exhaustive generation of some lattice paths and their prefixes

We refer to positive lattice paths as to paths in the discrete plane constituted by different kinds of steps (north-east, east and south-east), starting from the origin and never going under the x-axis. They have been deeply studied both from a combinatorial and an algorithmic point of view. We propose some algorithms for the exhaustive generation of positive paths which are Motzkin and Schröder paths and their prefixes, according to their length. For each kind of paths we define a recursive algorithm as well as an iterative one, specifying which path follows a given one in the lexicographic order. Furthermore we study the complexity of these algorithms by using the relations between the number of paths of a given size and the number of final north-east or south-east steps.

Counting the decimation classes of binary vectors with relatively prime length and density

We present a method for determining the number of decimation classes of density $$\delta $$ binary vectors indexed by a finite abelian group G of size $$\ell $$ and exponent $${\ell ^*}$$ such that $$\delta $$ is relatively prime to $${\ell ^*}$$ . This method is the first which is not based on exhaustive vector generation and exploits the subgroup lattice of $${{\mathbb {Z}}_{{\ell ^*}}^{\times }}$$ . Instead, our method is based on our newly developed theory of multipliers for arbitrary subsets of finite abelian groups, our results on orbits under the action of the multiplier group, and finding the number of solutions of a potentially highly symmetric subset sum problem. Implementing our method on vectors indexed by $${\mathbb {Z}}_{\ell }$$ of odd length $$\ell $$ and density $$(\ell +1)/2$$ greatly increased the number of $$\ell $$ for which the number of decimation classes of such vectors is known. Additionally, our newly developed theory provides information on the number of distinct translates fixed by each member of the multiplier group as well as sufficient conditions for each member of the multiplier group to be translate fixing.

The Unexpected Consequence of Incremental Design Changes

Human designers may find it difficult to anticipate the impact of small changes to some games, particularly in puzzle games. However, it is not difficult for computers to simulate all mechanical impacts of such small changes. This suggests that computers might be able to aid humans designers as they build and analyze game levels. This paper takes one step towards this larger goal by studying how Exhaustive Procedural Content Generation (EPCG) can be used for analysis of incremental changes of existing game levels. Using an incremental EPCG approach, we analyze all of the levels in the popular puzzle game Snakebird, showing that incremental variations in the level designs can significantly increase the length of the shortest possible solution. A user study on a subset of these modified levels shows that the modified levels are both interesting and challenging for humans to play. Thus, through the analysis of Snakebird, we demonstrate the broader potential for incremental applications of EPCG.

Two decades of trends in urban particulate matter concentrations across Australia

Australia is a highly developed country with low population density. Capital cities are situated mainly around the coastline and are subjected to different meteorological conditions. This complex set of drivers is expected to result in varying trends in particulate matter (PM) mass concentrations in urban ambient air across the country. Thus, the aim of this study was to determine the long-term trends in PM10 and PM2.5 concentrations in capital cities, and to analyse the factors that influenced such trends. The spatial variability of PM concentrations within the capital cities was first established to identify representative stations. Then trends were determined using the Mann-Kendall trend test, Sen's slope, and the generalised additive model. The results show that, in general, the PM concentrations in Australian cities are relatively low (12.1–21.7 μg m−3 mean daily PM10 and 4.6–8.7 μg m−3 mean daily PM2.5) and within the WHO daily limit 95% of the time. Over the past two decades, very small declines of 8.0 × 10−5–1.1 × 10−3 μg m−3.yr−1 for PM10 and 7.7 × 10−5–2.6 × 10−3 μg m−3.yr−1 for PM2.5 were observed while some stations exhibited increase in concentration based on available data; more stations showed a significant monotonic decline for PM10 than PM2.5. This is attributed to the effectiveness of the implemented emission reduction policies particularly for vehicle exhaust and power generation, given the simultaneous increase in the demand for energy and the number of vehicles over the last two decades. Regarding climate, in the coastal cities of Sydney and Brisbane, high rainfall and strong winds aid in maintaining low PM concentrations despite the significant anthropogenic emissions, while higher PM levels in Darwin can be attributed to its tropical savannah climate, which makes it prone to bushfires and necessitates regular prescribed burnings. PM concentrations increase when exceptional events such as bushfires and dust storms are induced by the extreme climate variability. Further reduction of PM concentrations in Australian cities is unlikely, considering the expanding urbanisation and the changing climate.

Efficient Algorithm for Generating Maximal L-Reflexive Trees

The line graph of a graph G is another graph of which the vertex set corresponds to the edge set of G, and two vertices of the line graph of G are adjacent if the corresponding edges in G share a common vertex. A graph is reflexive if the second-largest eigenvalue of its adjacency matrix is no greater than 2. Reflexive graphs give combinatorial ground to generate two classes of algebraic numbers, Salem and Pisot numbers. The difficult question of identifying those graphs whose line graphs are reflexive (called L-reflexive graphs) is naturally attacked by first answering this question for trees. Even then, however, an elegant full characterization of reflexive line graphs of trees has proved to be quite formidable. In this paper, we present an efficient algorithm for the exhaustive generation of maximal L-reflexive trees.

A Hybrid Artificial Bee Colony Strategy for t-way Test Set Generation with Constraints Support

t-way interaction testing is a systematic approach for exhaustive test set generation. It is a vital test planning method in software testing, which generates test sets based on interaction between parameters to cover every possible test sets combinations. t-way strategy clarifies the interaction strength between the number of parameters. However, there are some test sets combinations that should be excluded when generating the final test set as a result of invalid outputs, impossible or unwanted test sets combinations (e.g. system requirements set). These types of set combinations are known as constraint’s combinations or forbidden combinations. From existing studies, several t-way strategies have been proposed to address the test set combination problem, however, generating the optimal test set is still open research being an NP-hard problem. Therefore, this study proposed a novel hybrid artificial bee colony (HABC) t-way test set generation strategy with constraints support. The proposed approach is based on a hybrid artificial bee colony (ABC) algorithm with a particle swarm optimization (PSO) algorithm. PSO was integrated as the exploratory agent for the ABC hence the hybrid nature. The information sharing ability of PSO via the Weight Factor is used to enhance the performance of ABC. The output of the hybrid ABC is a set of promising optimal test set combinations. The results of the experiments showed that HABC outperformed and yielded better test sets than existing methods (HSS, LAHC, SA_SAT, PICT, TestCover, mATEG_SAT).

Constructions of Maximum Few-Distance Sets in Euclidean Spaces

A finite set of vectors $\mathcal{X}$ in the $d$-dimensional Euclidean space $\mathbb{R}^d$ is called an $s$-distance set if the set of mutual distances between distinct elements of $\mathcal{X}$ has cardinality exactly $s$. In this paper we present a combined approach of isomorph-free exhaustive generation of graphs and Gröbner basis computation to classify the largest $3$-distance sets in $\mathbb{R}^4$, the largest $4$-distance sets in $\mathbb{R}^3$, and the largest $6$-distance sets in $\mathbb{R}^2$. We also construct new examples of large $s$-distance sets in $\mathbb{R}^d$ for $d\leq 8$ and $s\leq 6$, and independently verify several earlier results from the literature.

Enumeration of relativistic states for superheavy and transactinide dimers in the periodic table

We have employed combinatorial techniques based on multinomial symmetric function (S-function) techniques for exhaustive enumeration and generation of relativistic (ω–ω states) states originating from relativistic 2-component molecular spinors for the seventh row superheavy dimers (Nh2-Ts2), transactinide dimers (Rf2-Rg2) and Ac2. The multinomial generators are so powerful that the complete set of relativistic states of all seventh row superheavy dimers or transactinide dimers are enumerated and constructed in a single generating function. We have computed and constructed the enumeration tables for all valence ω–ω states for the 7p-block and 6d-block dimers (Nh2-Ts2, Rf2-Rg2). Our results show that there are 6455 S-function terms giving rise to 102,830 valence ω–ω states- all arising only from the 6d shells of Bh2. Extension of the developed techniques to relativistic 4-component and 4-spinors arising from fermionic spin-3/2 particles are also suggested with potential applications NMR spectroscopy.

On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order

Abstract A generalized (resp. p-ary) ballot sequence is a sequence over the set of non-negative integers (resp. integers less than p) where in any of its prefixes each positive integer i occurs at most as often as any integer less than i. We show that the Reected Gray Code order induces a cyclic 3-adjacent Gray code on both, the set of fixed length generalized ballot sequences and p-ary ballot sequences when p is even, that is, ordered list where consecutive sequences (regarding the list cyclically) differ in at most 3 adjacent positions. Non-trivial efficient generating algorithms for these ballot sequences, in lexicographic order and for the obtained Gray codes, are also presented.

Exhaustive testing of safety-critical software for reactor protection system

As software is used to implement safety-critical functions in nuclear power plants (NPPs), the software developers must demonstrate that the software will generate its dedicated safety signal in on-demand situations based on proper test results to ensure the safety of digitalized NPP. This paper describes an automated exhaustive test case generation framework for the function block diagram (FBD) programs used in NPP safety systems. The proposed method translates an FBD program to a semantically equivalent satisfiability modulo theories (SMT) formula based on the formal definition of FBD and generates the exhaustive test cases given desired software output by iteratively solving the SMT formula. The effectiveness of the proposed framework is demonstrated with a case study of a trip logic software of a typical NPP reactor protection system. The case study results showed that the proposed approach could effectively generate exhaustive test cases and further prove that the NPP safety software is error-free in terms of its safety function.

Graphs with few hamiltonian cycles

We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number $k \ge 0$ of hamiltonian cycles, which is especially efficient for small $k$. Our main findings, combining applications of this algorithm and existing algorithms with new theoretical results, revolve around graphs containing exactly one hamiltonian cycle (1H) or exactly three hamiltonian cycles (3H). Motivated by a classic result of Smith and recent work of Royle, we show that there exist nearly cubic 1H graphs of order $n$ iff $n \ge 18$ is even. This gives the strongest form of a theorem of Entringer and Swart, and sheds light on a question of Fleischner originally settled by Seamone. We prove equivalent formulations of the conjecture of Bondy and Jackson that every planar 1H graph contains two vertices of degree 2, verify it up to order 16, and show that its toric analogue does not hold. We treat Thomassen's conjecture that every hamiltonian graph of minimum degree at least $3$ contains an edge such that both its removal and its contraction yield hamiltonian graphs. We also verify up to order 21 the conjecture of Sheehan that there is no 4-regular 1H graph. Extending work of Schwenk, we describe all orders for which cubic 3H triangle-free graphs exist. We verify up to order $48$ Cantoni's conjecture that every planar cubic 3H graph contains a triangle, and show that there exist infinitely many planar cyclically 4-edge-connected cubic graphs with exactly four hamiltonian cycles, thereby answering a question of Chia and Thomassen. Finally, complementing work of Sheehan on 1H graphs of maximum size, we determine the maximum size of graphs containing exactly one hamiltonian path and give, for every order $n$, the exact number of such graphs on $n$ vertices and of maximum size.

DNA barcoding of freshwater fishes from the transboundary river of Indo-Bhutan: multiple clades and cryptic diversity

The species diversity of freshwater fishes from the transboundary river, Jaldhaka is still unknown to the scientific communities. We generated 40 DNA barcode sequences of 16 morphologically identified freshwater fishes and compared genetically with the database sequences. Ten species (Acanthocobitis botia, Barilius bendelisis, Crossocheilus latius, Channa punctata, Channa quinquefasciata, Garra gotyla, Garra kempi, Opsarius barna, Psilorhynchus balitora, and Pseudecheneis sulcata) showed unique haplotypes in the studied riverine system. Further, the estimated genetic divergences, BA tree topology, and ABGD species delimitation methods revealed the presence of cryptic diversity in Badis badis, Garra annandalei, G. gotyla, G. kempi, P. balitora, Rasbora daniconius, and Pethia ticto. The study suggested more exhaustive sampling and generation of more molecular data to strengthen the fact. The aimed integrated approach will be helpful to detect the extant species diversity, helps to reevaluate the checklist and promote sustainable conservation management to protect this unparalleled ecosystem.