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A Practical Decision Procedure for Arithmetic with Function Symbols

Robert E. Shostak
1979 Journal of the ACM  
A practical procedure is presented for an extension of quantifier-free Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols This theory includes many of the formulas  ...  The extension of unquantified Presburger we shall be dealing with introduces, for each n _> 0, an unlimited number of n-ary function symbols (mterpreted as functions from Z n to Z) and n-ary predicate  ...  Spitzen for helpful discussions about this work.  ... 
doi:10.1145/322123.322137 fatcat:kjinrvaiebeqnkp5xer2eonnke

The UCLID Decision Procedure [chapter]

Shuvendu K. Lahiri, Sanjit A. Seshia
2004 Lecture Notes in Computer Science  
UCLID is a tool for term-level modeling and verification of infinite-state systems expressible in the logic of counter arithmetic with lambda expressions and uninterpreted functions (CLU).  ...  In this paper, we describe a key component of the tool, the decision procedure for CLU.  ...  Bryant for his invaluable support and feedback.  ... 
doi:10.1007/978-3-540-27813-9_40 fatcat:b764wtws7ner7epgz4izhx674y

$$\mathsf {SC}^\mathsf{2} $$ : Satisfiability Checking Meets Symbolic Computation [chapter]

Erika Ábrahám, John Abbott, Bernd Becker, Anna M. Bigatti, Martin Brain, Bruno Buchberger, Alessandro Cimatti, James H. Davenport, Matthew England, Pascal Fontaine, Stephen Forrest, Alberto Griggio (+3 others)
2016 Lecture Notes in Computer Science  
of decision procedures for arithmetic theories.  ...  Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application  ...  Acknowledgements We thank the anonymous reviewers for their comments.  ... 
doi:10.1007/978-3-319-42547-4_3 fatcat:lfizdur2sfdprjhgcycuac4zum

Satisfiability Modulo Theories: An Appetizer [chapter]

Leonardo de Moura, Nikolaj Bjørner
2009 Lecture Notes in Computer Science  
However, at their core is invariably a component using symbolic logic for describing states and transformations between them.  ...  It combines the problem of Boolean satisfiability with domains, such as, those studied in convex optimization and termmanipulating symbolic systems.  ...  Meta-Procedures It is infeasible to implement a (semi-) decision procedure for every possible theory that may be useful in practice.  ... 
doi:10.1007/978-3-642-10452-7_3 fatcat:wabzhnbstbcgphtptloaywgfxy

Page 1306 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
We believe that it is the integration of decision procedures with rewriting and induction which makes RRL effective for the application of reasoning about arithmetic circuits.”  ...  It is also shown how decision procedures can be augmented with induc- tion schemes extracted from a family of function definitions so that a certain subclass of conjectures can be automatically de- cided  ... 

The ICS Decision Procedures for Embedded Deduction [chapter]

Leonardo de Moura, Sam Owre, Harald Rueß, John Rushby, Natarajan Shankar
2004 Lecture Notes in Computer Science  
for example, requires simultaneously the theories of uninterpreted functions, linear arithmetic, and lists.  ...  ., nonlinear integer arithmetic) and those whose decision problems are often considered infeasible in practice (e.g., real closed fields) should not be ruled out completely.  ...  Core ICS The core algorithm of ICS is a corrected version of Shostak's combination procedure for equality and disequality with both uninterpreted and interpreted function symbols [11, 13] .  ... 
doi:10.1007/978-3-540-25984-8_14 fatcat:shrktb5z4ffbpkakpnkrvho4ly

Combining decision procedures by (model-)equality propagation

Diego Caminha B. de Oliveira, David Déharbe, Pascal Fontaine
2012 Science of Computer Programming  
useful decidable fragments such as uninterpreted symbols, linear arithmetic, and usual datastructures like arrays or lists.  ...  also on the generation of model equalities by decision procedures.  ...  Acknowledgements We are grateful to the anonymous reviewers for their remarks.  ... 
doi:10.1016/j.scico.2010.04.003 fatcat:m46t7qjkejaj3nl4ktnpkdj6ze

Combining Decision Procedures by (Model-)Equality Propagation

Diego Caminha B. de Oliveira, David Déharbe, Pascal Fontaine
2009 Electronical Notes in Theoretical Computer Science  
useful decidable fragments such as uninterpreted symbols, linear arithmetic, and usual datastructures like arrays or lists.  ...  also on the generation of model equalities by decision procedures.  ...  Acknowledgements We are grateful to the anonymous reviewers for their remarks.  ... 
doi:10.1016/j.entcs.2009.05.048 fatcat:tn6xxsm2qvfwfgjl67ez4ii2hm

Symbolic Execution for Checking the Accuracy of Floating-Point Programs

Jaideep Ramachandran, Corina Păsăreanu, Thomas Wahl
2015 Software engineering notes  
Our method is implemented in the Symbolic PathFinder tool and leverages and extends the floating-point decision procedure Realizer to check symbolic path constraints and to perform the accuracy checks.  ...  We present a symbolic execution approach to checking the accuracy of numerical programs, investigating how much a floating-point computation deviates from the "ideal" computation on real values.  ...  discussions and anonymous reviewers for helpful suggestions.  ... 
doi:10.1145/2693208.2693242 fatcat:bmorioclb5bhtap33gljvvwfc4

Functional Test Generation Using Constraint Logic Programming [chapter]

Zhihong Zeng, Maciej Ciesielski, Bruno Rouzeyre
2002 IFIP Advances in Information and Communication Technology  
The proposed SAT solver allows efficiently handling the designs with mixed word-level arithmetic operators and Boolean logic.  ...  Semi-formal verification based on symbolic simulation offers a good compromise between formal model checking and numerical simulation.  ...  possible decision tree in a unified solver, Figure 4 . 4 Functional test generation for design validation that works on CNF formulae.  ... 
doi:10.1007/978-0-387-35597-9_32 fatcat:uhmy4a7uxrgbnj2tq2eaiepclq

Interpolation for data structures

Deepak Kapur, Rupak Majumdar, Calogero G. Zarba
2006 Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering - SIGSOFT '06/FSE-14  
The approach taken is that of reducing the theories of such data structures to the theories of equality and linear arithmetic for which efficient interpolating decision procedures exist.  ...  We present efficient procedures to construct interpolants for the theories of arrays, sets, and multisets using the reduction approach for obtaining decision procedures for complex data structures.  ...  We thank Shriram Krishnamurthi and Corina Pasareanu for many detailed comments.  ... 
doi:10.1145/1181775.1181789 dblp:conf/sigsoft/KapurMZ06 fatcat:jgut44avzfd75mfa6vp4zwdiou

Automatic formal verification of DSP software

David W. Currie, Alan J. Hu, Sreeranga Rajan
2000 Proceedings of the 37th conference on Design automation - DAC '00  
By combining control-flow analysis, symbolic simulation, automatic decision procedures, and some domainspecific optimizations, we have built an automatic verification tool that compares structurally similar  ...  This paper describes a novel formal verification approach for equivalence checking of small, assembly-language routines for digital signal processors (DSP).  ...  The verification method is based on a combination of control flow analysis, symbolic simulation, and cooperating decision procedures for memory, linear arithmetic, and uninterpreted functions with equality  ... 
doi:10.1145/337292.337339 dblp:conf/dac/CurrieHR00 fatcat:grohhw4vkrgqrj6yvg7cw5ei6q

Zap: Automated Theorem Proving for Software Analysis [chapter]

Thomas Ball, Shuvendu K. Lahiri, Madanlal Musuvathi
2005 Lecture Notes in Computer Science  
We describe our desiderata for such an interface to an ATP, the logics (theories) that an ATP for program analysis should support, and present how we have incorporated many of these ideas in Zap, an ATP  ...  Automated theorem provers (ATPs) are a key component that many software verification and program analysis tools rely on.  ...  The theories present in Zap are the logic of equality with uninterpreted functions (EUF) and linear arithmetic. The decision procedure for EUF is based on the congruence closure algorithm [NO80] .  ... 
doi:10.1007/11591191_2 fatcat:uczhvijn6vew3bmwpaqhaxrkzy

Modeling and Verifying Systems Using a Logic of Counter Arithmetic with Lambda Expressions and Uninterpreted Functions [chapter]

Randal E. Bryant, Shuvendu K. Lahiri, Sanjit A. Seshia
2002 Lecture Notes in Computer Science  
We give theoretical and empirical evidence for the efficiency of our decision procedure.  ...  In this paper, we present the logic of Counter Arithmetic with Lambda Expressions and Uninterpreted Functions (CLU).  ...  The third author was supported in part by a National Defense Science and Engineering Graduate Fellowship.  ... 
doi:10.1007/3-540-45657-0_7 fatcat:77cmw5bmkrasrpcxijkxnfwe4y

Little Engines of Proof [chapter]

Natarajan Shankar
2002 Lecture Notes in Computer Science  
The other school, pioneered by Hao Wang, argues for problem-specific combinations of decision and semi-decision procedures.  ...  In recent years, several high quality inference engines have been developed, including propositional satisfiability solvers, ground decision procedures for equality and arithmetic, quantifier elimination  ...  Automated reasoning got off to a running start in the 1950s. Already in 1954, Davis [Dav57] had implemented a decision procedure for Presburger arithmetic [Pre29] .  ... 
doi:10.1007/3-540-45614-7_1 fatcat:6my3fmm6xjb4vfj6sxly46xbxa
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