Alternating register automata on finite words and trees

Figueira, Diego

doi:10.2168/lmcs-8(1:22)2012

Cited by 31 publications

(30 citation statements)

References 29 publications

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“…However, the emptiness problem for ARA with 1 register (cf. monadic predicate automata) was proved to be decidable in [11] by reduction to reachability for lossy counter machines; and a direct proof based on well-structured transition systems was later presented in [16].…”

Section: Related Workmentioning

confidence: 99%

Proof Spaces for Unbounded Parallelism

Farzan

Kincaid

Podelski

2015

Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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In this paper, we present a new approach to automatically verify multi-threaded programs which are executed by an unbounded number of threads running in parallel.The starting point for our work is the problem of how we can leverage existing automated verification technology for sequential programs (abstract interpretation, Craig interpolation, constraint solving, etc.) for multi-threaded programs. Suppose that we are given a correctness proof for a trace of a program (or for some other program fragment). We observe that the proof can always be decomposed into a finite set of Hoare triples, and we ask what can be proved from the finite set of Hoare triples using only simple combinatorial inference rules (without access to a theorem prover and without the possibility to infer genuinely new Hoare triples)?We introduce a proof system where one proves the correctness of a multi-threaded program by showing that for each trace of the program, there exists a correctness proof in the space of proofs that are derivable from a finite set of axioms using simple combinatorial inference rules. This proof system is complete with respect to the classical proof method of establishing an inductive invariant (which uses thread quantification and control predicates). Moreover, it is possible to algorithmically check whether a given set of axioms is sufficient to prove the correctness of a multi-threaded program, using ideas from well-structured transition systems.

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Section: Related Workmentioning

confidence: 99%

Proof Spaces for Unbounded Parallelism

Farzan

Kincaid

Podelski

2015

Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…This approach, albeit in a limited form, was already proposed in e.g. [15]. The details of the construction can be found in the appendix.…”

Section: Conclusion and Other Modelsmentioning

confidence: 99%

Regular Expressions with Binding over Data Words for Querying Graph Databases

Libkin

Tan

Vrgoč

2013

Developments in Language Theory

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Abstract. Data words assign to each position a letter from a finite alphabet and a data value from an infinite set. Introduced as an abstraction of paths in XML documents, they recently found applications in querying graph databases as well. Those are actively studied due to applications in such diverse areas as social networks, semantic web, and biological databases. Querying formalisms for graph databases are based on specifying paths conforming to some regular conditions, which led to a study of regular expressions for data words.Previously studied regular expressions for data words were either rather limited, or had the full expressiveness of register automata, at the expense of a quite unnatural and unintuitive binding mechanism for data values. Our goal is to introduce a natural extension of regular expressions with proper bindings for data values, similar to the notion of freeze quantifiers used in connection with temporal logics over data words, and to study both language-theoretic properties of the resulting class of languages of data words, and their applications in querying graph databases.

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“…Tree automata with registers to store and compare data values were studied in [20] as an extension to a similar model on words [19,22]. A decidable alternating version of these automata called ATRA was studied in [18], and it was extended in [9,12] to show decidability of the satisfiability problem for forward-XPath. The work [3] introduces a simple yet powerful automata model called Class Automata on data trees that can capture FO 2 (< h , succ h , <v, succv, ∼), XPath, ATRA, and other models.…”

Section: Automatamentioning

confidence: 99%

“…• The forward fragment of XPath, extending the downward fragment with the next sibling and the following sibling axes, is decidable with non-primitive recursive complexity [9,12].…”

Section: Xpathmentioning

confidence: 99%

On XPath with transitive axes and data tests

Figueira

2013

Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We study the satisfiability problem for XPath with data equality tests. XPath is a node selecting language for XML documents whose satisfiability problem is known to be undecidable, even for very simple fragments. However, we show that the satisfiability for XPath with the rightward, leftward and downward reflexive-transitive axes (namely followingsibling-or-self, preceding-sibling-or-self, descendant-or-self) is decidable. Our algorithm yields a complexity of 3ExpSpace, and we also identify an expressive-equivalent normal form for the logic for which the satisfiability problem is in 2Exp-Space. These results are in contrast with the undecidability of the satisfiability problem as soon as we replace the reflexive-transitive axes with just transitive (non-reflexive) ones.

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Alternating register automata on finite words and trees

Cited by 31 publications

References 29 publications

Proof Spaces for Unbounded Parallelism

Proof Spaces for Unbounded Parallelism

Regular Expressions with Binding over Data Words for Querying Graph Databases

On XPath with transitive axes and data tests

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