scholarly journals Clause Elimination for SAT and QSAT

2015 ◽  
Vol 53 ◽  
pp. 127-168 ◽  
Author(s):  
Marijn Heule ◽  
Matti Järvisalo ◽  
Florian Lonsing ◽  
Martina Seidl ◽  
Armin Biere
Keyword(s):  
Normal Form ◽  
Real World ◽  
Practical Importance ◽  
Empirical Evaluation ◽  
Conjunctive Normal Form ◽  
Boolean Satisfiability ◽  
Practical Applications ◽  
Logical Equivalence ◽  
Hard Problems ◽  
Simplification Techniques

The famous archetypical NP-complete problem of Boolean satisfiability (SAT) and its PSPACE-complete generalization of quantified Boolean satisfiability (QSAT) have become central declarative programming paradigms through which real-world instances of various computationally hard problems can be efficiently solved. This success has been achieved through several breakthroughs in practical implementations of decision procedures for SAT and QSAT, that is, in SAT and QSAT solvers. Here, simplification techniques for conjunctive normal form (CNF) for SAT and for prenex conjunctive normal form (PCNF) for QSAT---the standard input formats of SAT and QSAT solvers---have recently proven very effective in increasing solver efficiency when applied before (i.e., in preprocessing) or during (i.e., in inprocessing) satisfiability search. In this article, we develop and analyze clause elimination procedures for pre- and inprocessing. Clause elimination procedures form a family of (P)CNF formula simplification techniques which remove clauses that have specific (in practice polynomial-time) redundancy properties while maintaining the satisfiability status of the formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on asymmetric variants of these techniques, and also develop a novel family of so-called covered clause elimination procedures, as well as natural liftings of the CNF-level procedures to PCNF. We analyze the considered clause elimination procedures from various perspectives. Furthermore, for the variants not preserving logical equivalence under clause elimination, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs, which is important for practical applications for the procedures. Complementing the more theoretical analysis, we present results on an empirical evaluation on the practical importance of the clause elimination procedures in terms of the effect on solver runtimes on standard real-world application benchmarks. It turns out that the importance of applying the clause elimination procedures developed in this work is empirically emphasized in the context of state-of-the-art QSAT solving.

Chapter 9. Preprocessing in SAT Solving

2021 ◽  
Author(s):  
Armin Biere ◽  
Matti Järvisalo ◽  
Benjamin Kiesl
Keyword(s):  
Normal Form ◽  
Conjunctive Normal Form ◽  
Boolean Satisfiability ◽  
Sat Solving ◽  
Speed Up ◽  
Sat Solver ◽  
Main Ideas ◽  
Simplification Techniques

Preprocessing has become a key component of the Boolean satisfiability (SAT) solving workflow. In practice, preprocessing is situated between the encoding phase and the solving phase, with the aim of decreasing the total solving time by applying efficient simplification techniques on SAT instances to speed up the search subsequently performed by a SAT solver. In this chapter, we overview key preprocessing techniques proposed in the literature. While the main focus is on techniques applicable to formulas in conjunctive normal form (CNF), we also selectively cover main ideas for preprocessing structural and higher-level SAT instance representations.

scholarly journals A Reduction based Method for Coloring Very Large Graphs

2017 ◽  
Author(s):  
Jinkun Lin ◽  
Shaowei Cai ◽  
Chuan Luo ◽  
Kaile Su
Keyword(s):  
Lower Bound ◽  
Real World ◽  
Upper Bound ◽  
Practical Importance ◽  
Optimal Solution ◽  
Large Graphs ◽  
Graph Coloring Problem ◽  
Hard Problems ◽  
Novel Method ◽  
Novel Concept

The graph coloring problem (GCP) is one of the most studied NP hard problems and has numerous applications. Despite the practical importance of GCP, there are limited works in solving GCP for very large graphs. This paper explores techniques for solving GCP on very large real world graphs.We first propose a reduction rule for GCP, which is based on a novel concept called degree bounded independent set.The rule is iteratively executed by interleaving between lower bound computation and graph reduction. Based on this rule, we develop a novel method called FastColor, which also exploits fast clique and coloring heuristics. We carry out experiments to compare our method FastColor with two best algorithms for coloring large graphs we could find. Experiments on a broad range of real world large graphs show the superiority of our method. Additionally, our method maintains both upper bound and lower bound on the optimal solution, and thus it proves an optimal solution when the upper bound meets the lower bound. In our experiments, it proves the optimal solution for 97 out of 142 instances.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

scholarly journals A Novel Rail-Network Hardware Simulator for Embedded System Programming

Electronics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 13
Author(s):  
Balaji M ◽  
Chandrasekaran M ◽  
Vaithiyanathan Dhandapani
Keyword(s):  
Embedded Systems ◽  
Embedded System ◽  
Real Time ◽  
Learning Outcomes ◽  
Real World ◽  
Time Constraints ◽  
Network Simulator ◽  
Practical Applications ◽  
Rail Network ◽  
Knowledge Enhancement

A Novel Rail-Network Hardware with simulation facilities is presented in this paper. The hardware is designed to facilitate the learning of application-oriented, logical, real-time programming in an embedded system environment. The platform enables the creation of multiple unique programming scenarios with variability in complexity without any hardware changes. Prior experimental hardware comes with static programming facilities that focus the students’ learning on hardware features and programming basics, leaving them ill-equipped to take up practical applications with more real-time constraints. This hardware complements and completes their learning to help them program real-world embedded systems. The hardware uses LEDs to simulate the movement of trains in a network. The network has train stations, intersections and parking slots where the train movements can be controlled by using a 16-bit Renesas RL78/G13 microcontroller. Additionally, simulating facilities are provided to enable the students to navigate the trains by manual controls using switches and indicators. This helps them get an easy understanding of train navigation functions before taking up programming. The students start with simple tasks and gradually progress to more complicated ones with real-time constraints, on their own. During training, students’ learning outcomes are evaluated by obtaining their feedback and conducting a test at the end to measure their knowledge acquisition during the training. Students’ Knowledge Enhancement Index is originated to measure the knowledge acquired by the students. It is observed that 87% of students have successfully enhanced their knowledge undergoing training with this rail-network simulator.

scholarly journals Non Stationary Multi-Armed Bandit: Empirical Evaluation of a New Concept Drift-Aware Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 380
Author(s):  
Emanuele Cavenaghi ◽  
Gabriele Sottocornola ◽  
Fabio Stella ◽  
Markus Zanker
Keyword(s):  
Real World ◽  
Concept Drift ◽  
Empirical Evaluation ◽  
Sliding Window ◽  
Discount Factor ◽  
Data Streaming ◽  
Sources Of Information ◽  
Sequential Decision ◽  
Time Step ◽  
Thompson Sampling

The Multi-Armed Bandit (MAB) problem has been extensively studied in order to address real-world challenges related to sequential decision making. In this setting, an agent selects the best action to be performed at time-step t, based on the past rewards received by the environment. This formulation implicitly assumes that the expected payoff for each action is kept stationary by the environment through time. Nevertheless, in many real-world applications this assumption does not hold and the agent has to face a non-stationary environment, that is, with a changing reward distribution. Thus, we present a new MAB algorithm, named f-Discounted-Sliding-Window Thompson Sampling (f-dsw TS), for non-stationary environments, that is, when the data streaming is affected by concept drift. The f-dsw TS algorithm is based on Thompson Sampling (TS) and exploits a discount factor on the reward history and an arm-related sliding window to contrast concept drift in non-stationary environments. We investigate how to combine these two sources of information, namely the discount factor and the sliding window, by means of an aggregation function f(.). In particular, we proposed a pessimistic (f=min), an optimistic (f=max), as well as an averaged (f=mean) version of the f-dsw TS algorithm. A rich set of numerical experiments is performed to evaluate the f-dsw TS algorithm compared to both stationary and non-stationary state-of-the-art TS baselines. We exploited synthetic environments (both randomly-generated and controlled) to test the MAB algorithms under different types of drift, that is, sudden/abrupt, incremental, gradual and increasing/decreasing drift. Furthermore, we adapt four real-world active learning tasks to our framework—a prediction task on crimes in the city of Baltimore, a classification task on insects species, a recommendation task on local web-news, and a time-series analysis on microbial organisms in the tropical air ecosystem. The f-dsw TS approach emerges as the best performing MAB algorithm. At least one of the versions of f-dsw TS performs better than the baselines in synthetic environments, proving the robustness of f-dsw TS under different concept drift types. Moreover, the pessimistic version (f=min) results as the most effective in all real-world tasks.

The problem of simplifying logical expressions

1959 ◽  
Vol 24 (1) ◽  
pp. 17-19 ◽  
Author(s):  
B. Dunham ◽  
R. Fridshal
Keyword(s):  
Normal Form ◽  
Simplification Techniques

By quite elementary means, one can find “large” examples difficult, if not (for practical purposes) impossible, to be managed by that host of methods, after Quine, for minimizing expressions in alternational normal form. Because the workability rather than existence of an algorithm for minimizing logical formulae is generally critical, it may be pertinent to outline briefly the derivation of these “large” examples. Some more general insight may also be gained about simplification techniques.

A reduction class containing formulas with one monadic predicate and one binary function symbol

1976 ◽  
Vol 41 (1) ◽  
pp. 45-49
Author(s):  
Charles E. Hughes
Keyword(s):  
Normal Form ◽  
Predicate Symbol ◽  
Conjunctive Normal Form ◽  
Function Symbol ◽  
Predicate Calculus ◽  
Binary Function ◽  
First Order ◽  
The Matrix ◽  
Reduction Class ◽  
Order Predicate Calculus

AbstractA new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀x∀yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

scholarly journals Source identification of infectious diseases in networks via label ranking

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245344
Author(s):  
Jianye Zhou ◽  
Yuewen Jiang ◽  
Biqing Huang
Keyword(s):  
Infectious Diseases ◽  
Real World ◽  
Source Identification ◽  
Human Society ◽  
Practical Applications ◽  
Ranking Algorithms ◽  
Label Ranking ◽  
Infection Source ◽  
And Control ◽  
Complete Observation

Background Outbreaks of infectious diseases would cause great losses to the human society. Source identification in networks has drawn considerable interest in order to understand and control the infectious disease propagation processes. Unsatisfactory accuracy and high time complexity are major obstacles to practical applications under various real-world situations for existing source identification algorithms. Methods This study attempts to measure the possibility for nodes to become the infection source through label ranking. A unified Label Ranking framework for source identification with complete observation and snapshot is proposed. Firstly, a basic label ranking algorithm with complete observation of the network considering both infected and uninfected nodes is designed. Our inferred infection source node with the highest label ranking tends to have more infected nodes surrounding it, which makes it likely to be in the center of infection subgraph and far from the uninfected frontier. A two-stage algorithm for source identification via semi-supervised learning and label ranking is further proposed to address the source identification issue with snapshot. Results Extensive experiments are conducted on both synthetic and real-world network datasets. It turns out that the proposed label ranking algorithms are capable of identifying the propagation source under different situations fairly accurately with acceptable computational complexity without knowing the underlying model of infection propagation. Conclusions The effectiveness and efficiency of the label ranking algorithms proposed in this study make them be of practical value for infection source identification.

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