Reflexive transitive invariant relations: A basis for computing loop functions

Mili, Ali; Aharon, Shir; Nadkarni, Chaitanya; Jilani, Lamia Labed; Louhichi, Asma; Mraihi, Olfa

doi:10.1016/j.jsc.2008.11.007

Cited by 10 publications

(4 citation statements)

References 28 publications

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“…the number of disjuncts, and their merging). [24,6,21] or variance analyses [5] (recently described in literature for proving termination), which describe relationships between a state at a program location and any other (as opposed to immediately) previous state at that location. Hence, theoretically, progress invariants are more precise in the sense that transition invariants can be generated from progress invariants but not vice-versa.…”

Section: Related Workmentioning

confidence: 99%

Control-flow refinement and progress invariants for bound analysis

GulwaniSumit¹,

JainSagar²,

KoskinenEric³

2009

SIGPLAN Not.

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Symbolic complexity bounds help programmers understand the performance characteristics of their implementations. Existing work provides techniques for statically determining bounds of procedures with simple control-flow. However, procedures with nested loops or multiple paths through a single loop are challenging.In this paper we describe two techniques, control-flow refinement and progress invariants, that together enable estimation of precise bounds for procedures with nested and multi-path loops. Control-flow refinement transforms a multi-path loop into a semantically equivalent code fragment with simpler loops by making the structure of path interleaving explicit. We show that this enables non-disjunctive invariant generation tools to find a bound on many procedures for which previous techniques were unable to prove termination. Progress invariants characterize relationships between consecutive states that can arise at a program location. We further present an algorithm that uses progress invariants to compute precise bounds for nested loops. The utility of these two techniques goes beyond our application to symbolic bound analysis. In particular, we discuss applications of control-flow refinement to proving safety properties that otherwise require disjunctive invariants.We have applied our methodology to over 670,000 lines of code of a significant Microsoft product and were able to find symbolic bounds for 90% of the loops. We are not aware of any other published results that report experiences running a bound analysis on a real code-base.

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Section: Related Workmentioning

confidence: 99%

Control-flow refinement and progress invariants for bound analysis

GulwaniSumit¹,

JainSagar²,

KoskinenEric³

2009

SIGPLAN Not.

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“…The study of invariant assertions, and more broadly the functional analysis of programs, have been the focus of active research in the seventies and eighties, and the subject of renewed interest in the last few years [1,6,7,9,20,23,37,39,40,61]. In this paper we wish to investigate the relationships between this well known, thoroughly researched, concept, and two distinct but related concepts: invariant functions [52] and invariant relations [50].…”

Section: Introductionmentioning

confidence: 99%

Invariant assertions, invariant relations, and invariant functions

Mraihi

Louhichi

Jilani

et al. 2013

Science of Computer Programming

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“…We have shown in [11] that from an invariant relation we can infer an invariant assertion. We have not found a way to infer an invariant relation from an invariant assertion, because invariant assertions are unary relations whereas invariant relations are binary relations.…”

Section: Relations Between Invariants 41 Invariant Assertions and Inmentioning

confidence: 99%

“…The study of invariant assertions, and their use in the analysis of while loops, have been the focus of active research in the seventies and eighties, and the subject of renewed interest in the last few years. In this paper we wish to investigate the relationships between this well known, thoroughly researched, concept, and two distinct but related concepts: invariant functions [12] and invariant relations [9]. We consider a while loop w on space S defined by w = while t do B.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Invariant Assertions, Invariant Relations, and Invariant Functions

Louhichi¹,

Mraihi²,

Jilani³

et al.

EPiC Series in Computing

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Invariant assertions play an important role in the analysis and documentation of while loops of imperative programs. Invariant functions and invariant relations are alternative analysis tools that are distinct from invariant assertions but are related to them. In this paper we discuss these three concepts and analyze their relationships. The study of invariant functions and invariant relations is interesting not only because it provides alternative means to analyze loops, but also because it gives us insights into the structure of invariant assertions, and may help us enhance techniques for generating invariant assertions.

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Reflexive transitive invariant relations: A basis for computing loop functions

Cited by 10 publications

References 28 publications

Control-flow refinement and progress invariants for bound analysis

Control-flow refinement and progress invariants for bound analysis

Invariant assertions, invariant relations, and invariant functions

A Comparative Study of Invariant Assertions, Invariant Relations, and Invariant Functions

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