Conjunctive abstract interpretation using paramodulation

Or Ozeri*, Oded Padon, Noam Rinetzky, Mooly Sagiv

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Scaling static analysis is one of the main challenges for program verification in general and for abstract interpretation in particular. One way to compactly represent a set of states is using a formula in conjunctive normal form (CNF). This can sometimes save exponential factors. Therefore, CNF formulae are commonly used in manual program verification and symbolic reasoning. However, it is not used in abstract interpretation, due to the complexity of reasoning about the effect of program statements when the states are represented this way. We present algorithms for performing abstract interpretation on CNF formulae recording equality and inequalities of ground terms. Here, terms correspond to the values of variables and of addresses and contents of dynamically allocated memory locations, and thus, a formula can represent pointer equalities and inequalities. The main idea is the use of the rules of paramodulation as a basis for an algorithm that computes logical consequences of CNF formulae, and the application of the algorithm to perform joins and transformers. The algorithm was implemented and used for reasoning about low level programs. We also show that our technique can be used to implement best transformers for a variant of Connection Analysis via a nonstandard interpretation of equality.

Original languageEnglish
Title of host publicationVerification, Model Checking, and Abstract Interpretation - 18th International Conference, VMCAI 2017, Proceedings
EditorsAhmed Bouajjani, David Monniaux
PublisherSpringer Verlag
Pages442-461
Number of pages20
ISBN (Print)9783319522333
DOIs
StatePublished - 2017
Event18th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2017 - Paris, France
Duration: 15 Jan 201717 Jan 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10145 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2017
Country/TerritoryFrance
CityParis
Period15/01/1717/01/17

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