## Tableau Method

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### Noriaki Yoshiura - One of the best experts on this subject based on the ideXlab platform.

• ##### stepwise satisfiability checking procedure for reactive system specifications by Tableau Method and proof system
International Conference on Formal Engineering Methods, 2012
Co-Authors: Yoshinori Neya, Noriaki Yoshiura
Abstract:

Open reactive systems are systems that ideally never terminate and are intended to maintain some interaction with their environment. Temporal logic is one of the Methods for formal specification description of open reactive systems. For an open reactive system specification, we do not always obtain a program satisfying it because the open reactive system program must satisfy the specification no matter how the environment of the open reactive system behaves. This problem is known as realizability and the complexity of realizability check is double or triple exponential time of the length of specification formula and realizability checking of specifications is impractical. This paper implements stepwise satisfiability checking procedure with Tableau Method and proof system. Stepwise satisfiability is one of the necessary conditions of realizability of reactive system specifications. The implemented procedure uses proof system that is introduced in this paper. This proof system can accelerate the decision procedure, but since it is imcomplete it cannot itself decide the realizability property of specifications. The experiment of this paper shows that the implemented procedure can decide the realizability property of several specifications.

• ##### ICFEM - Stepwise satisfiability checking procedure for reactive system specifications by Tableau Method and proof system
Formal Methods and Software Engineering, 2012
Co-Authors: Yoshinori Neya, Noriaki Yoshiura
Abstract:

Open reactive systems are systems that ideally never terminate and are intended to maintain some interaction with their environment. Temporal logic is one of the Methods for formal specification description of open reactive systems. For an open reactive system specification, we do not always obtain a program satisfying it because the open reactive system program must satisfy the specification no matter how the environment of the open reactive system behaves. This problem is known as realizability and the complexity of realizability check is double or triple exponential time of the length of specification formula and realizability checking of specifications is impractical. This paper implements stepwise satisfiability checking procedure with Tableau Method and proof system. Stepwise satisfiability is one of the necessary conditions of realizability of reactive system specifications. The implemented procedure uses proof system that is introduced in this paper. This proof system can accelerate the decision procedure, but since it is imcomplete it cannot itself decide the realizability property of specifications. The experiment of this paper shows that the implemented procedure can decide the realizability property of several specifications.

### Gernot Stenz - One of the best experts on this subject based on the ideXlab platform.

• ##### dctp 1 2 system abstract
Theorem Proving with Analytic Tableaux and Related Methods, 2002
Co-Authors: Gernot Stenz
Abstract:

We describe version 1.2 of the theorem prover DCTP, which is an implementation of the disconnection calculus. The disconnection calculus is a confluent Tableau Method using non-rigid variables. This current version of DCTP has been extended and enhanced significantly since its participation in the IJCAR system competition in 2001. We briefly sketch the underlying calculus and the proof procedure and describe some of its refinements and new features. We also present the results of some experiments regarding these new features.

• ##### TableauX - DCTP 1.2 - System Abstract
Lecture Notes in Computer Science, 2002
Co-Authors: Gernot Stenz
Abstract:

We describe version 1.2 of the theorem prover DCTP, which is an implementation of the disconnection calculus. The disconnection calculus is a confluent Tableau Method using non-rigid variables. This current version of DCTP has been extended and enhanced significantly since its participation in the IJCAR system competition in 2001. We briefly sketch the underlying calculus and the proof procedure and describe some of its refinements and new features. We also present the results of some experiments regarding these new features.

• ##### dctp a disconnection calculus theorem prover system abstract
International Joint Conference on Automated Reasoning, 2001
Co-Authors: Reinhold Letz, Gernot Stenz
Abstract:

We describe the theorem prover DCTP, which is an implementation of the disconnection Tableau calculus, a confluent Tableau Method, in which free variables are treated in a non-rigid manner. In contrast to most other free-variable Tableau variants, the system can also be used for model generation. We sketch the underlying calculus and its refinements, and present the results of an experimental evaluation.

• ##### IJCAR - DCTP - A Disconnection Calculus Theorem Prover - System Abstract
Automated Reasoning, 2001
Co-Authors: Reinhold Letz, Gernot Stenz
Abstract:

We describe the theorem prover DCTP, which is an implementation of the disconnection Tableau calculus, a confluent Tableau Method, in which free variables are treated in a non-rigid manner. In contrast to most other free-variable Tableau variants, the system can also be used for model generation. We sketch the underlying calculus and its refinements, and present the results of an experimental evaluation.

### Yoshinori Neya - One of the best experts on this subject based on the ideXlab platform.

• ##### stepwise satisfiability checking procedure for reactive system specifications by Tableau Method and proof system
International Conference on Formal Engineering Methods, 2012
Co-Authors: Yoshinori Neya, Noriaki Yoshiura
Abstract:

Open reactive systems are systems that ideally never terminate and are intended to maintain some interaction with their environment. Temporal logic is one of the Methods for formal specification description of open reactive systems. For an open reactive system specification, we do not always obtain a program satisfying it because the open reactive system program must satisfy the specification no matter how the environment of the open reactive system behaves. This problem is known as realizability and the complexity of realizability check is double or triple exponential time of the length of specification formula and realizability checking of specifications is impractical. This paper implements stepwise satisfiability checking procedure with Tableau Method and proof system. Stepwise satisfiability is one of the necessary conditions of realizability of reactive system specifications. The implemented procedure uses proof system that is introduced in this paper. This proof system can accelerate the decision procedure, but since it is imcomplete it cannot itself decide the realizability property of specifications. The experiment of this paper shows that the implemented procedure can decide the realizability property of several specifications.

• ##### ICFEM - Stepwise satisfiability checking procedure for reactive system specifications by Tableau Method and proof system
Formal Methods and Software Engineering, 2012
Co-Authors: Yoshinori Neya, Noriaki Yoshiura
Abstract:

Open reactive systems are systems that ideally never terminate and are intended to maintain some interaction with their environment. Temporal logic is one of the Methods for formal specification description of open reactive systems. For an open reactive system specification, we do not always obtain a program satisfying it because the open reactive system program must satisfy the specification no matter how the environment of the open reactive system behaves. This problem is known as realizability and the complexity of realizability check is double or triple exponential time of the length of specification formula and realizability checking of specifications is impractical. This paper implements stepwise satisfiability checking procedure with Tableau Method and proof system. Stepwise satisfiability is one of the necessary conditions of realizability of reactive system specifications. The implemented procedure uses proof system that is introduced in this paper. This proof system can accelerate the decision procedure, but since it is imcomplete it cannot itself decide the realizability property of specifications. The experiment of this paper shows that the implemented procedure can decide the realizability property of several specifications.

### Ilkka Niemela - One of the best experts on this subject based on the ideXlab platform.

• ##### unrestricted vs restricted cut in a Tableau Method for boolean circuits
Annals of Mathematics and Artificial Intelligence, 2005
Co-Authors: Matti Jarvisalo, Tommi Junttila, Ilkka Niemela
Abstract:

This paper studies the relative efficiency of variations of a Tableau Method for Boolean circuit satisfiability checking. The considered Method is a nonclausal generalisation of the Davis---Putnam---Logemann---Loveland (DPLL) procedure to Boolean circuits. The variations are obtained by restricting the use of the cut (splitting) rule in several natural ways. It is shown that the more restricted variations cannot polynomially simulate the less restricted ones. For each pair of Methods T, T?, an infinite family $\{\mathcal{C}_{n}\}$ of circuits is devised for which T has polynomial size proofs while in T? the minimal proofs are of exponential size w.r.t. n, implying exponential separation of T and T? w.r.t. n. The results also apply to DPLL for formulas in conjunctive normal form obtained from Boolean circuits by using Tseitin's translation. Thus DPLL with the considered cut restrictions, such as allowing splitting only on the variables corresponding to the input gates, cannot polynomially simulate DPLL with unrestricted splitting.

• ##### ISAIM - Unrestricted vs restricted cut in a Tableau Method for Boolean circuits
Annals of Mathematics and Artificial Intelligence, 2005
Co-Authors: Matti Jarvisalo, Tommi Junttila, Ilkka Niemela
Abstract:

This paper studies the relative efficiency of variations of a Tableau Method for Boolean circuit satisfiability checking. The considered Method is a nonclausal generalisation of the Davis---Putnam---Logemann---Loveland (DPLL) procedure to Boolean circuits. The variations are obtained by restricting the use of the cut (splitting) rule in several natural ways. It is shown that the more restricted variations cannot polynomially simulate the less restricted ones. For each pair of Methods T, T?, an infinite family $\{\mathcal{C}_{n}\}$ of circuits is devised for which T has polynomial size proofs while in T? the minimal proofs are of exponential size w.r.t. n, implying exponential separation of T and T? w.r.t. n. The results also apply to DPLL for formulas in conjunctive normal form obtained from Boolean circuits by using Tseitin's translation. Thus DPLL with the considered cut restrictions, such as allowing splitting only on the variables corresponding to the input gates, cannot polynomially simulate DPLL with unrestricted splitting.

• ##### Computational Logic - Towards an Efficient Tableau Method for Boolean Circuit Satisfiability Checking
Computational Logic — CL 2000, 2000
Co-Authors: Tommi Junttila, Ilkka Niemela
Abstract:

Boolean circuits offer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a Tableau Method for solving satisfiability problems for Boolean circuits is devised. The Method employs a direct cut rule combined with deterministic deduction rules. Simplification rules for circuits and a search heuristic attempting to minimize the search space are developed. Experiments in symbolic model checking domain indicate that the Method is competitive against state-of-the-art satisfiability checking techniques and a promising basis for further work.

• ##### towards an efficient Tableau Method for boolean circuit satisfiability checking
Lecture Notes in Computer Science, 2000
Co-Authors: Tommi Junttila, Ilkka Niemela
Abstract:

Boolean circuits offer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a Tableau Method for solving satisfiability problems for Boolean circuits is devised. The Method employs a direct cut rule combined with deterministic deduction rules. Simplification rules for circuits and a search heuristic attempting to minimize the search space are developed. Experiments in symbolic model checking domain indicate that the Method is competitive against state-of-the-art satisfiability checking techniques and a promising basis for further work.

• ##### Towards an Ecient Tableau Method for
2000
Co-Authors: Tommi Junttila, Ilkka Niemela
Abstract:

Boolean circuits oer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a Tableau Method for solving satisability problems for Boolean cir- cuits is devised. The Method employs a direct cut rule combined with de- terministic deduction rules. Simplication rules for circuits and a search heuristic attempting to minimize the search space are developed. Ex- periments in symbolic model checking domain indicate that the Method is competitive against state-of-the-art satisability checking techniques and a promising basis for further work.

### Naoki Yonezaki - One of the best experts on this subject based on the ideXlab platform.

• ##### FTRTFT - Derivation of the Input Conditional Formula from a Reactive System Specifictaion in Temporal Logic
Lecture Notes in Computer Science, 1994
Co-Authors: Ryosei Mori, Naoki Yonezaki
Abstract:

We present an algorithm which derives the input conditional formula from a reactive system specification. The input conditional formula explicitly expresses the constraints on the environment behavior which are implicitly involved in an unrealizable specification. The input conditional formula provides useful information in the specification/synthesis process for reactive systems. We use propositional linear-time temporal logic as a specification language, and our derivation algorithm is based on the Tableau Method for temporal logic.