Counting in Trees for Free

Seidl, Helmut; Schwentick, Thomas; Muscholl, Anca; Habermehl, Peter

doi:10.1007/978-3-540-27836-8_94

Cited by 77 publications

(127 citation statements)

References 23 publications

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“…Several lines of work closely resemble those for node-labeled trees: e.g., [DLM04] introduced Presburger conditions on children, defined an automaton model, and proved decidability, similarly to [SSM03,SS+04].…”

Section: 2mentioning

confidence: 99%

“…We now define MSO mod [Cou90] as an extension of MSO with modulo quantifiers: for each set variable X, and k > 1, we have set new formulae Q k (X) which are true iff the cardinality of X is congruent to 0 modulo k. Further extensions in terms of arithmetic power have been considered in [SSM03,SS+04]. Recall that Presburger arithmetic refers to the FO theory of the structure N, + , and it is known that this structure admits quantifier elimination in the vocabulary (+, <, 0, 1, (∼ k ) k∈N ) where n ∼ k m iff n − m = 0(mod k).…”

Section: 2mentioning

confidence: 99%

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Logics for Unranked Trees: An Overview

Libkin

2005

Automata, Languages and Programming

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Abstract. Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees.

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Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Logics for Unranked Trees: An Overview

Libkin

2005

Automata, Languages and Programming

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“…This set of conjuncts ensures that each computation corresponds to a traversal of the graphs of the processes. This is inspired by the construction of an existential Presburger formula for the Parikh image of the language of finite-state automata [30].…”

Section: Translationmentioning

confidence: 99%

Analysis of Message Passing Programs Using SMT-Solvers

Abdulla

Atig

Cederberg

2013

Automated Technology for Verification and Analysis

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Abstract. We consider message passing programs where processes communicate asynchronously over unbounded channels. The reachability problem for such systems are either undecidable or have very high complexity. In order to achieve efficiency, we consider the phase-bounded reachability problem, where each process is allowed to perform a bounded number of phases during a run of the system. In a given phase, the process is allowed to perform send or receive transitions (but not both). We present a uniform framework where the channels are assigned different types of semantics such as lossy, stuttering, or unordered. We show that the framework allows a uniform translation of bounded-phase reachability for each of the above mentioned semantics to the satisfiability of quantifierfree Presburger formulas. This means that we can use the full power of modern SMT-solvers for efficient analysis of our systems. Furthermore, we show that the translation implies that bounded-phase reachability is NP-COMPLETE. Finally, we prove that the problem becomes undecidable if we allow perfect channels or push-down processes communicating through (stuttering) lossy channels. We report on the result of applying the prototype on a number of non-trivial examples.

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“…Tree automata were intensively studied in the literature, in particular for program veri cation, where tree automata provide abstraction-based approximations of program con gurations. In this direction, several classes of extended automata were de ned in order to provide ner approximations [4,12,10,17,33,24,31,23].…”

Section: Conclusion and Related Workmentioning

confidence: 99%

TAGED Approximations for Temporal Properties Model-Checking

Courbis

Héam

Kouchnarenko

2009

Implementation and Application of Automata

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Abstract. This paper investigates the use of tree automata with global equalities and disequalities (TAGED for short) in reachability analysis over term rewriting systems (TRSs). The reachability problem being in general undecidable on non terminating TRSs, we provide TAGEDbased construction, and then design approximation-based semi-decision procedures to model-check useful temporal patterns on in nite state rewriting graphs. To show that the above TAGED-based construction can be e ectively carried out, complexity analysis for rewriting TAGEDde nable languages is given. Recently, reachability analysis turned out to be a very e cient veri cation technique for proving properties on in nite systems modeled by term rewriting systems (TRSs for short). In the rewriting theory, the reachability problem is the following: given a TRS R and two terms s and t, can we decide whether s → * R t or not? This problem, which can easily be solved on strongly terminating TRSs, is undecidable on non terminating TRSs. However, on the one hand, there exist several syntactic classes of TRSs for which this problem becomes decidable [16,20,34]. On the other hand, in addition to classical proof tools of rewriting, given a set E ⊆ T (F) of initial terms, provided that s ∈ E, one can prove s → * R t by using over-approximations of R * (E) [21,16] and proving that t does not belong to these approximations. Recently, the veri cation of temporal properties of systems modeled by TRSs has been investigated [15,28,27]. To apply these very interesting and promising theoretical results to applications This work has been funded by the French ANR-06-SETI-014 RAVAJ project.

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Counting in Trees for Free

Cited by 77 publications

References 23 publications

Logics for Unranked Trees: An Overview

Logics for Unranked Trees: An Overview

Analysis of Message Passing Programs Using SMT-Solvers

TAGED Approximations for Temporal Properties Model-Checking

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