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A Generalization of Stålmarck's Method [chapter]

Aditya Thakur, Thomas Reps
2012 Lecture Notes in Computer Science  
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]

Byron Cook, Georges Gonthier
2005 Lecture Notes in Computer Science  
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

G. Andersson, P. Bjesse, B. Cook, Z. Hanna
2003 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
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

Gunnar Andersson, Per Bjesse, Byron Cook, Ziyad Hanna
2002 Proceedings - Design Automation Conference  
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]

Parosh Aziz Abdulla, Per Bjesse, Niklas Eén
2000 Lecture Notes in Computer Science  
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]

Natarajan Shankar
2002 Lecture Notes in Computer Science  
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]

Thomas Reps, Aditya Thakur
2015 Lecture Notes in Computer Science  
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]

Pierre Letouzey, Laurent Théry
2000 Lecture Notes in Computer Science  
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]

Phillip James, Andy Lawrence, Faron Moller, Markus Roggenbach, Monika Seisenberger, Anton Setzer, Karim Kanso, Simon Chadwick
2014 Lecture Notes in Computer Science  
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

Chu-Min Li
2003 Discrete Applied Mathematics  
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]

Lintao Zhang, Sharad Malik
2002 Lecture Notes in Computer Science  
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]

Lintao Zhang, Sharad Malik
2002 Lecture Notes in Computer Science  
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

Koen Claessen, Niklas Een, Mary Sheeran, Niklas Sorensson
2008 2008 9th International Workshop on Discrete Event Systems  
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]

Nachum Dershowitz, Jieh Hsiang, Guan-Shieng Huang, Daher Kaiss
2006 Lecture Notes in Computer Science  
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]

Marijn J. H. Heule, Matti Järvisalo, Armin Biere
2013 Lecture Notes in Computer Science  
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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