• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.87-109
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• 2002

A satisfiability problem in propositional logic is the problem of checking for the existence of a set of truth values of atomic prepositions that renders an input propositional formula true. This paper describes an empirical investigation of a particular integer programming approach, using the set covering model, to solve satisfiability problems. Our satisfiability engine, SETSAT, is a fully integrated, linear programming based, branch and bound method using various symbolic routines for the reduction of the logic formulas. SETSAT has been implemented in the integer programming shell MINTO which, in turn, uses the CPLEX linear programming system. The logic processing routines were written in C and integrated into the MINTO functions. The experiments were conducted on a benchmark set of satisfiability problems that were compiled at the University of Ulm in Germany. The computational results indicate that our approach is competitive with the state of the art.

• Journal of Information Processing Systems
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• v.13 no.5
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• pp.1149-1157
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• 2017

The satisfiability problem is always a core problem in artificial intelligence (AI). And how to improve the efficiency of algorithms solving the satisfiability problem is widely concerned. Algorithm IER (Improved Extension Rule) is based on extension rule. The number of atoms and the number of clauses affect the efficiency of the algorithm IER. DPLL rules are helpful to reduce these numbers. Then a complete algorithm CIER based on splitting rule and extension rule is proposed in this paper in order to improve the efficiency. At first, the algorithm CIER (Complete Improved Extension Rule) reduces the scale of a clause set with DPLL rules. Then, the clause set is split into a group of small clause sets. In the end, the satisfiability of the clause set is got from these small clause sets'. A strategy MOAMD (maximum occurrences and maximum difference) for the algorithm CIER is given. With this strategy, a better arrangement of atoms could be got. This arrangement could make the number of small clause sets fewer and the scale of these sets smaller. So, the algorithm CIER will be more efficient.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.200-207
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• 2013

Petri Nets are a system description and analysis tool. Reachability is one of the most basic properties in Petri Net research. In a sense, reachability research is the foundation study for other dynamic properties of Petri Nets through which many problems involving Petri Nets can be described. Nowadays, there are two mature analysis methods-the matrix equation and the reachability tree. However, both methods are localized, i.e., it is difficult to find a general algorithm that can determine reachability for an arbitrary Petri Net, especially an unbounded Petri Net. This paper proposes and proves three propositions in order to present a subclass of a Petri Net, the live single-branch Petri Net, whose reachability is equivalent to the satisfiability of the state equation.

• Journal of Internet Computing and Services
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• v.9 no.2
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• pp.89-105
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• 2008

So far, most of research on automated test data generation(ATDG) deals with programs without pointers. Recently, few works hove been done on ATDG in the presence of pointers, but they ore path-oriented techniques which require the specification of on entire program path to be tested or a program to be executed. This paper presents a new technique for generating test data even without specifying a program path completely. The presented technique is a static technique which transforms the test data generation problem into a SAT(SATisfiability) problem and makes advantage of SAT solvers for ATDG. For the ends, we transform a program under test into Alloy which is the first-order relational logic and then produce test data via Alloy analyzer.

• The KIPS Transactions:PartD
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• v.15D no.6
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• pp.777-784
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• 2008

Recently in the field of model checking, to overcome the state explosion problem, the method of using a SAT-solver is mainly researched. To use a SAT-solver, the system to be verified is translated into CNF and the Boolean cardinality constraint is widely used in translating the system into CNF. In BCC it is dealt with set of boolean variables, but there is no translating method of the sequence among Boolean variables. In this paper, we propose methods for translating the problem, which is extracting a subsequence with length k from a sequence of Boolean variables, into CNF formulas. Through experimental results, we show that our method is more efficient than using only BCC.

• The KIPS Transactions:PartD
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• v.16D no.6
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• pp.911-920
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• 2009

Airbone software must comply the DO-178B standard in order to be certified by the FAA. The standard requires the unit testing of safety-critical software to meet the coverage criterion called MC/DC(Modified Condition/Decision Coverage). Although MC/DC is known to be effective in finding errors related to safety, it is also true that generating test cases which satisfy the MC/DC criterion is not easy. This paper presents a tool named MD-SAT which generates MC/DC test cases with SAT(SATisfiability) technology. It can be employed for generating diverse test cases in tools implementing various testing techniques including decision table based test, cause-effect graphing, and state-based test.

• The KIPS Transactions:PartD
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• v.16D no.3
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• pp.371-380
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• 2009

Recently, lots of research on automated test data generation has been actively done. However, techniques for automated test data generation presented so far have been proved ineffective for programs with flag variables. It can present problems when considering embedded systems such as engine controllers that make extensive use of flag variables to record state information concerning devices. This paper introduces a technique for generating test data effectively for programs with flag variables. The presented technique transforms the test data generation problem into a SAT(SATisfiability) problem and makes advantage of SAT solvers for automated test data generation(ATDG). For the ends, we transform a program under test into Alloy which is the first-order relational logic and then produce test data via Alloy analyzer.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.881-883
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• 2003

하드웨어 검증과 모델 체킹 등의 분야에서, SAT(satisfiability problem)나 항진 명제 검사(tautology checking)는 매우 중요한 문제이다. 그러나 이들은 모두 NP-complete 문제이므로 그 복잡도가 매우 크다. 이를 해결하기 위해 여러 가지 연구가 이루어져 왔으며, 여러 효율적인 알고리즘이 존재한다. 이러한 알고리즘은 대부분 일반 표현식을 CNF(conjunctive normal form)로 바꾸어 입력 형식으로 사용한다. 이 논문에서는 일반 표현식을 입력으로 받아 DNF로 변환한 뒤 DNF의 특성을 이용하여 SAT를 검사하는 효율적인 방법을 제시한다.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.517-519
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• 2003

하드웨어 검증과 모델 체킹 등의 분야에서, SAT(satisfiability problem)나 항진 명제 검사(tautology checking)는 매우 중요한 문제이다. 그러나 이들은 모두 NP-complete 문제이므로 그 복잡도가 매우 크다. 이를 해결하기 위한 여러 연구가 진행되고 있고, 그 결과 성능이 좋은 solver들이 개발되었다. 하지만 문제가 커질수록 solver의 처리 시간이 급격하게 증가한다. 이 논문에서는 solver가 복잡한 문제를 더 효율적으로 풀기 위해 논문“Local search for Boolean relations on the basis of unit propagation”［5］에서 제안된 preprocessor(전처리기), P_EQ의 개념을 설명하고, 실험을 통한 결과를 제시한다.

• KIPS Transactions on Software and Data Engineering
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• v.6 no.6
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• pp.293-302
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• 2017

This paper proposes a method that generates test cases from Simulink/Stateflow(SL/SF) using a SMT (Satisfiability Modulo Theory) solver, Yices and information of SL/SF model. The most difficult problem to generate test cases from SL/SF model is to solve reachability problem. In the propose method, Yices and the tables built with the model information are utilized to solve the reachability problem. The method utilizes the SMT model, that is the SL/SF model transformed in Yices. The tables built from SL/SF are used for backward processing of the proposed method and increases test generation efficiency. A commercial refrigerator model and two car ECU (Electrical Control Unit) models are used to evaluate the performance of the proposed algorithm..