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A Generalization of Stålmarck's Method
[chapter]
2012
Lecture Notes in Computer Science
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Stålmarck's method is one instantiation of the framework; other instantiations lead to new decision procedures for propositional logic. ...
This paper gives an account of Stålmarck's method for validity checking of propositional-logic formulas, and explains each of the key components in terms of concepts from the field of abstract interpretation ...
Björk [2] explored extensions of Stålmarck's method to first-order logic. ...
doi:10.1007/978-3-642-33125-1_23
fatcat:wb24fdmlj5fx7jw3osuld7sr6m
Using Stålmarck's Algorithm to Prove Inequalities
[chapter]
2005
Lecture Notes in Computer Science
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Stålmarck's 1-saturation algorithm is an incomplete but fast method for computing partial equivalence relations over propositional formulae. ...
In this paper we characterize a set of formulae with bitvector-inequalities for which 1-saturation is sufficient to prove unsatisfiability. ...
As in [12] , we use the notation R(x ≡ y) to represent a union operation over the equivalence classes in the PER. ...
doi:10.1007/11576280_23
fatcat:famael6wdbbermltjvmafkyh6e
Design automation with mixtures of proof strategies for propositional logic
2003
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Design automation problems can often be encoded in propositional logic, and solved by applying propositional logic proof methods. ...
By defining our proof engine in such a way that we can compose strategies to form new, more powerful, strategies we achieve synergistic effects between the individual methods. ...
The authors would like to thank Arne Borälv and Gunnar Stålmarck for their comments and suggestions. Koen Claessen worked with us on a preliminary version of the tool CAPTAIN PROVE [17] . ...
doi:10.1109/tcad.2003.814959
fatcat:os3at2bczfgi5ayqqflkmrflhy
A proof engine approach to solving combinational design automation problems
2002
Proceedings - Design Automation Conference
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By defining our proof engine in such a way that we can compose strategies to form new, more powerful, strategies we achieve synergistic effects between the individual methods. ...
In this paper, we present a proof engine framework where individual analyses are viewed as strategies-functions between different proof states. ...
The ideas behind tactics and tacticals have since proved to be fruitful enough that most theorem provers for first order and higher-order logics use variations on this approach. ...
doi:10.1145/513918.514101
dblp:conf/dac/AnderssonBCH02
fatcat:odnnqydaafdh7grw4rtxvkyu2y
Symbolic Reachability Analysis Based on SAT-Solvers
[chapter]
2000
Lecture Notes in Computer Science
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In a parallel development, SAT-solving procedures, such as Stålmarck's method or the Davis-Putnam procedure, have been used successfully in verifying very large industrial systems. ...
Although BDDs have played a crucial role in this success, they have some well-known drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications ...
Thanks to Purushothaman Iyer, Bengt Jonsson, Gordon Pace, Mary Sheeran and Gunnar Stålmarck for giving valuable feedback on earlier drafts. ...
doi:10.1007/3-540-46419-0_28
fatcat:hkwlgzseajbuhplwqsyf4ce7fy
Little Engines of Proof
[chapter]
2002
Lecture Notes in Computer Science
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We focus in particular on combining different decision procedures for use in automated verification. Its great triumph was to prove that the sum of two even numbers is even. ...
procedures for integers and reals, and abstraction methods for finitely approximating problems over infinite domains. ...
The popularity of uniform proof methods like resolution stems from the simple dogma that since first-order logic is a generic language for expressing statements, generic first-order proof search methods ...
doi:10.1007/3-540-45614-7_1
fatcat:6my3fmm6xjb4vfj6sxly46xbxa
Automating Abstract Interpretation
[chapter]
2015
Lecture Notes in Computer Science
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This paper describes a twenty-year quest by the first author to address this issue by raising the level of automation in abstract interpretation. ...
Reps has an ownership interest in GrammaTech, Inc., which has licensed elements of the technology reported in this publication. ...
Reps would like to thank the many people with whom he collaborated on the work described in the paper (as well as work that motivated the work described): for shape analysis: M. Sagiv, R. ...
doi:10.1007/978-3-662-49122-5_1
fatcat:ox4jxxxeprgidcvimvltq4svq4
Formalizing Stålmarck's Algorithm in Coq
[chapter]
2000
Lecture Notes in Computer Science
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We present the development of a machine-checked implementation of Stålmarck's algorithm. First, we prove the correctness and the completeness of an abstract representation of the algorithm. ...
The algorithm Stålmarck's algorithm is a tautology checker. ...
In order to define an evaluation on triplets, we first need to define an evaluation on rZ as: Definition rZEval : (nat → bool ) → rZ → bool := λf: nat → bool . λr: rZ . ...
doi:10.1007/3-540-44659-1_24
fatcat:gkivphalwjcpfg7thquwzfrqdu
Verification of Solid State Interlocking Programs
[chapter]
2014
Lecture Notes in Computer Science
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We report on the inclusion of a formal method into a design process in industry. ...
We present a complete methodology for carrying out this verification step in the case of ladder logic programs and give results for real world railway interlockings. ...
properties expressed in first order logic, their specialization to propositional logic, and their satisfaction relative to the labelled transition system. ...
doi:10.1007/978-3-319-05032-4_19
fatcat:wjm4tsayvzgwxc3enjtfwcttzm
Equivalent literal propagation in the DLL procedure
2003
Discrete Applied Mathematics
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equivalent literals in F in order to get other equivalent literals and to simplify F. ...
We propose a simple data structure to represent all equivalent literals such as l1 ↔ l2 in a CNF formula F, and implement a special look-ahead technique, called equivalency reasoning, to propagate these ...
Purdom for their help to improve the English of this paper. ...
doi:10.1016/s0166-218x(02)00407-9
fatcat:otaygmxcdnhtvcnw4gggsjkvom
The Quest for Efficient Boolean Satisfiability Solvers
[chapter]
2002
Lecture Notes in Computer Science
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In this paper we examine some of the main ideas along this passage that have led to our current capabilities. ...
Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. ...
Acknowledgments The authors would like to thank Dr. Aarti Gupta for suggestions and help in improving the paper. ...
doi:10.1007/3-540-45620-1_26
fatcat:2e4iv7jfxvbklhthmhuqj7q62m
The Quest for Efficient Boolean Satisfiability Solvers
[chapter]
2002
Lecture Notes in Computer Science
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In this paper we examine some of the main ideas along this passage that have led to our current capabilities. ...
Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. ...
Acknowledgments The authors would like to thank Dr. Aarti Gupta for suggestions and help in improving the paper. ...
doi:10.1007/3-540-45657-0_2
fatcat:szmpyakmd5e35hlfjzrpzeibf4
SAT-solving in practice
2008
2008 9th International Workshop on Discrete Event Systems
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Satisfiability solving, the problem of deciding whether the variables of a propositional formula can be assigned in such a way that the formula evaluates to true, is one of the classic problems in computer ...
In this tutorial paper, we show briefly how such SAT-solvers are implemented, and point to some typical applications of them. ...
acknowledge Joao Marques-Silva for useful comments on earlier drafts of this paper, and Bengt Lennartson and Martin Fabian from the Signals and Systems Department at Chalmers for taking the initiative to ...
doi:10.1109/wodes.2008.4605923
fatcat:c3w2p5n2ena33aozdweue4eklq
Boolean Rings for Intersection-Based Satisfiability
[chapter]
2006
Lecture Notes in Computer Science
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We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stålmarck. ...
We propose a combined linear and binomial representation for Booleanring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. ...
Acknowledgement We are grateful to the referees for their comments. ...
doi:10.1007/11916277_33
fatcat:vnbvfmtbrrec3lbdcpwkhmxwzu
Revisiting Hyper Binary Resolution
[chapter]
2013
Lecture Notes in Computer Science
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Experiments show that our implementation improves the performance of state-of-the-art CNFlevel SAT techniques on combinational equivalent checking instances. ...
Then let the solver restart, and afterward assign similarly first g = 0 and then g = 1 in order to learn the clause (g ∨ ¬g). ...
{(a, d) , (¬b, e)}, which means that both of these non-transitive hyper binary resolvents can be added to F while maintaining logical equivalence. Example 2. ...
doi:10.1007/978-3-642-38171-3_6
fatcat:yagoze3senahrlcjdi4zflctha
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