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Program Analysis Using Quantifier-Elimination Heuristics [chapter]

Deepak Kapur
2012 Lecture Notes in Computer Science  
Quantifier elimination heuristics can be developed using which it is possible to generate constraints on lower and upper bounds by table look ups in O(n 2 ) steps, where n is the number of program variables  ...  Miné gave well-designed algorithms based on Difference Bound Matrices (DBMs) and graph representation for performing various operations needed for program analysis using the abstract interpretation approach  ...  Summary Quantifier-elimination heuristics might be an alternative to abstract interpretation for program analysis.  ... 
doi:10.1007/978-3-642-29952-0_15 fatcat:xyqsewwevjetzktyhmonhb6wx4

Abstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis (Extended Version) [article]

Kengo Kido, Swarat Chaudhuri, Ichiro Hasuo
2015 arXiv   pre-print
We extend abstract interpretation for the purpose of verifying hybrid systems.  ...  2) employing Robinson's nonstandard analysis (NSA) to define mathematically rigorous semantics.  ...  We thank Kohei Suenaga and the anonymous referees for useful discussions and comments.  ... 
arXiv:1511.00825v1 fatcat:d24dm2ct6ndsbaulmrsmkf5t34

Language Design Issues for Agents based on Linear Logic (Extended Abstract)

James Harland, Michael Winikoff
2002 Electronical Notes in Theoretical Computer Science  
One way to bridge this gap is to re-cast the foundations of such systems into a logic programming framework.  ...  Agent systems based on the Belief, Desire and Intention model of Rao and Georgeff have been used for a number of successful applications.  ...  Hence the use of modus ponens in linear logic is more like a committed choice, in that once the inference rule is applied, p is no longer available, but q is, and so our analysis needs to proceed in a  ... 
doi:10.1016/s1571-0661(04)80590-5 fatcat:yutmovcdj5di5hcsbacq6jdlkm

On the reliability of usability testing

Martin Kessner, Jo Wood, Richard F. Dillon, Robert L. West
2001 CHI '01 extended abstracts on Human factors in computer systems - CHI '01  
Kendall's coefficient of concordance between the eleven evaluators serving in a Heuristic Evaluation was W(39) = -3 1, p < .O1 (Nielsen, 1994) .  ...  FirstIy, the product to be tested was a four-year-old Windows program that was well developed. Second, the testing tearns couldn't communicate with the deveIopment team at alI.  ...  Users expect cancel to be the furthest bucton o n the right, particularly since help is not considered to be particulariy useful. (36) Tltere is no feedback on ivlziclz skorrcur location is active.  ... 
doi:10.1145/634126.634127 fatcat:ruhklk7pfbehdgv4d3hqz6noyy

Geometric Quantifier Elimination Heuristics for Automatically Generating Octagonal and Max-plus Invariants [chapter]

Deepak Kapur, Zhihai Zhang, Matthias Horbach, Hengjun Zhao, Qi Lu, ThanhVu Nguyen
2013 Lecture Notes in Computer Science  
Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as  ...  Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astrée tool based on abstract interpretation framework  ...  With these considerations in mind, it can be shown that program analysis using our geometric heuristic for quantifier elimination for octagons takes quadratic time in the number of program variables: Theorem  ... 
doi:10.1007/978-3-642-36675-8_11 fatcat:azi6olpq6fbllpgacgoeqhvzle

Nonlinear Polynomials, Interpolants and Invariant Generation for System Analysis

Deepak Kapur
2017 International Symposium on Symbolic and Algebraic Computation  
While we have been investigating methods based on symbolic computation algorithms including Gröbner basis and approximate quantifier elimination for over a decade (see  ...  While there has recently been considerable interest in researching heuristics for generating loops invariants, almost all developments have focused on generating invariants typically handled using SMT  ...  We discuss various heuristics based on elimination for automatically generating loop invariants, termination analysis, interpolant generation and related constructions found useful for static program analysis  ... 
dblp:conf/issac/Kapur17 fatcat:byuzsz2cmfaxngnvfsugwo6rfq

SAFARI: SMT-Based Abstraction for Arrays with Interpolants [chapter]

Francesco Alberti, Roberto Bruttomesso, Silvio Ghilardi, Silvio Ranise, Natasha Sharygina
2012 Lecture Notes in Computer Science  
A heuristics, called term abstraction, favors the convergence of the tool by "tuning" interpolants and guessing additional quantified variables of invariants to prune the search space efficiently.  ...  We present SAFARI, a model checker designed to prove (possibly universally quantified) safety properties of imperative programs with arrays of unknown length.  ...  Introduction Efficient and automatic static analysis of imperative programs is still an open challenge.  ... 
doi:10.1007/978-3-642-31424-7_49 fatcat:jvi32v743zhnrkgp3mdabhqsje

Zap: Automated Theorem Proving for Software Analysis [chapter]

Thomas Ball, Shuvendu K. Lahiri, Madanlal Musuvathi
2005 Lecture Notes in Computer Science  
Automated theorem provers (ATPs) are a key component that many software verification and program analysis tools rely on.  ...  We believe that program analysis clients would benefit greatly if theorem provers were to provide a richer set of operations.  ...  In practice, we have found that our implementation is limited by the heuristics we use to instantiate quantifiers.  ... 
doi:10.1007/11591191_2 fatcat:uczhvijn6vew3bmwpaqhaxrkzy

InvGen: An Efficient Invariant Generator [chapter]

Ashutosh Gupta, Andrey Rybalchenko
2009 Lecture Notes in Computer Science  
InvGen's unique feature is in its use of dynamic analysis to make invariant generation order of magnitude more efficient. 1 See [5] for the syntax of transition relations.  ...  In this paper we present InvGen, an automatic linear arithmetic invariant generator for imperative programs.  ...  After the elimination of program variables InvGen obtains the constraints λ ≥ 0 ∧ −λ = α n ∧ α ≥ 0, where λ is an existentially quantified variable. λ does not appear anywhere in the constraint and can  ... 
doi:10.1007/978-3-642-02658-4_48 fatcat:efvq2tef6rgdvjzvsezrbq4tli

Predicate abstraction for software verification

Cormac Flanagan, Shaz Qadeer
2002 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '02  
Our method is based on predicate abstraction, an abstract interpretation technique in which the abstract domain is constructed from a given set of predicates over program variables.  ...  A novel feature of our approach is that it infers universally-quantified loop invariants, which are crucial for verifying programs that manipulate unbounded data such as arrays.  ...  that enabled us to implement and evaluate our ideas.  ... 
doi:10.1145/503272.503291 dblp:conf/popl/FlanaganQ02 fatcat:ulirgqrjhjhu7dlrxogv526mdu

Predicate abstraction for software verification

Cormac Flanagan, Shaz Qadeer
2002 SIGPLAN notices  
Our method is based on predicate abstraction, an abstract interpretation technique in which the abstract domain is constructed from a given set of predicates over program variables.  ...  A novel feature of our approach is that it infers universally-quantified loop invariants, which are crucial for verifying programs that manipulate unbounded data such as arrays.  ...  that enabled us to implement and evaluate our ideas.  ... 
doi:10.1145/565816.503291 fatcat:i6woyl74gzekxizrbcsnvbeipu

Path invariants

Dirk Beyer, Thomas A. Henzinger, Rupak Majumdar, Andrey Rybalchenko
2007 SIGPLAN notices  
There are two advantages to using such path programs as counterexamples for abstraction refinement.  ...  First, we can bring the whole machinery of program analysis to bear on path programs, which are typically small compared to the original program.  ...  However, these techniques either require the user to specify the assertions (often with Skolem constants for the quantified variables) [19] , or use heuristics to derive quantifiers by generalization  ... 
doi:10.1145/1273442.1250769 fatcat:ajrdlcefafe2zdvcvvvhxs4uge

Path invariants

Dirk Beyer, Thomas A. Henzinger, Rupak Majumdar, Andrey Rybalchenko
2007 Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation - PLDI '07  
There are two advantages to using such path programs as counterexamples for abstraction refinement.  ...  First, we can bring the whole machinery of program analysis to bear on path programs, which are typically small compared to the original program.  ...  However, these techniques either require the user to specify the assertions (often with Skolem constants for the quantified variables) [19] , or use heuristics to derive quantifiers by generalization  ... 
doi:10.1145/1250734.1250769 dblp:conf/pldi/BeyerHMR07 fatcat:h6pofhspy5atvis35jrovhhusi

Proofs by Deduction [chapter]

2017 Logic and Language Models for Computer Science  
Many use models as certificates for satisfiability to extract feasible program executions; others use proof objects as certificates for unsatisfiability in the context of highintegrity systems development  ...  This report documents the program and the outcomes of Dagstuhl Seminar 15381 "Information from Deduction: Models and Proofs".  ...  Compositional Program Analysis using Max-SMT Currently we are extending the framework to prove reachability properties by using conditional termination.  ... 
doi:10.1142/9789813229211_0003 fatcat:cqpgqtobz5gx3db5bq54gxrd4m

Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)

Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, Cesare Tinelli, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17371 "Deduction Beyond First-Order Logic."  ...  We discussed different abstractions and refinement strategies for reasoning with large first-order theories.  ...  Since then I have been investigating how to develop heuristics for quantifier elimination to generate interpolants.  ... 
doi:10.4230/dagrep.7.9.26 dblp:journals/dagstuhl-reports/BlanchetteFST17 fatcat:yfc3wk2fwngc3i2dmjwrz3gsgi
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