Verification of Graph Transformation Systems with Context-Free Specifications

König, Barbara; Esparza, Javier

doi:10.1007/978-3-642-15928-2_8

Cited by 12 publications

(7 citation statements)

References 25 publications

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“…This approach has been used successfully in verification [19], [21], [26], [28], [31], and it seems natural to extend it to querying paths in graph databases.…”

Section: Introductionmentioning

confidence: 99%

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Figueira

Libkin

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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We study logics expressing properties of paths in graphs that are tailored to querying graph databases: a data model for new applications such as social networks, the Semantic Web, biological data, crime detection, and others. The basic construct of such logics, a regular path query, checks for paths whose labels belong to a regular language. These logics fail to capture two commonly needed features: counting properties, and the ability to compare paths. It is known that regular path-comparison relations (e.g., prefix or equality) can be added without significant complexity overhead; however, adding common relations often demanded by applications (e.g., subword, subsequence, suffix) results in either undecidability or astronomical complexity.We propose, as a way around this problem, to use automata with counting functionalities, namely Parikh automata. They express many counting properties directly, and they approximate many relations of interest. We prove that with Parikh automata defining both languages and relations used in queries, we retain the low complexity of the standard path logics for graphs. In particular, this gives us efficient approximations to queries with prohibitively high complexity. We extend the best known decidability results by showing that even more expressive classes of relations are possible in query languages (sometimes with restriction on the shape of formulae). We also show that Parikh automata admit two convenient representations by analogs of regular expressions, making them usable in real-life querying.

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“…This approach has been used successfully in verification [19], [21], [26], [28], [31], and it seems natural to extend it to querying paths in graph databases.…”

Section: Introductionmentioning

confidence: 99%

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Figueira

Libkin

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

show abstract

“…Many problems in computer science and software engineering can be modelled in terms of rule-based graph transformations [13], motivating research into verifying the correctness of grammars and programs based on this unit of computation. Various approaches towards this goal have been proposed, with techniques including model checking [9], unfoldings [4,16], k-induction [29], weakest preconditions [10,11], abstract interpretation [17], and program logics [5,24,25].…”

Section: Introductionmentioning

confidence: 99%

Incorrectness Logic for Graph Programs

Poskitt

2021

Preprint

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Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning, which has the promise of better scalability. In this paper, we present an under-approximate program logic for a nondeterministic graph programming language, and show how it can be used to reason deductively about program incorrectness, whether defined by the presence of forbidden graph structure or by finitely failing executions. We prove this 'incorrectness logic' to be sound and complete, and speculate on some possible future applications of it.

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“…Since the classical automata-based approach to modelchecking [28], finite automata have been extended in many ways to tackle the automatic verification of more realistic and powerful systems against more expressive specifications. For instance, they have been extended to pushdown systems [3,26,30], concurrent systems [5], and systems with counters or specifications with arithmetic constraints have been the focus of many works in verification [7,11,[15][16][17][18]23].…”

Section: Introductionmentioning

confidence: 99%

Two-Way Parikh Automata with a Visibly Pushdown Stack

Dartois

Filiot

Talbot

2019

Lecture Notes in Computer Science

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In this paper, we investigate the complexity of the emptiness problem for Parikh automata equipped with a pushdown stack. Pushdown Parikh automata extend pushdown automata with counters which can only be incremented and an acceptance condition given as a semilinear set, which we represent as an existential Presburger formula over the final values of the counters. We show that the non-emptiness problem both in the deterministic and non-deterministic cases is NP-c. If the input head can move in a two-way fashion, emptiness gets undecidable, even if the pushdown stack is visibly and the automaton deterministic. We define a restriction, called the single-use restriction, to recover decidability in the presence of two-wayness, when the stack is visibly. This syntactic restriction enforces that any transition which increments at least one dimension is triggered only a bounded number of times per input position. Our main contribution is to show that non-emptiness of twoway visibly Parikh automata which are single-use is NExpTime-c. We finally give applications to decision problems for expressive transducer models from nested words to words, including the equivalence problem.

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Verification of Graph Transformation Systems with Context-Free Specifications

Cited by 12 publications

References 25 publications

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Incorrectness Logic for Graph Programs

Two-Way Parikh Automata with a Visibly Pushdown Stack

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