Alternation-free modal mu-calculus for data trees

Jurdziński, Marcin; Lazić, Ranko

doi:10.1109/lics.2007.11

Cited by 39 publications

(34 citation statements)

References 29 publications

(56 reference statements)

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“…More recent work has focused specifically on data as a source of infinity. This includes augmenting recursive procedures with integer parameters [12], rewriting systems with data [11], Petri nets with data associated to tokens [33], automata and logics over infinite alphabets [36,10,11], and temporal logics manipulating data [13,22,31]. However, the restricted use of data and the particular properties verified have limited applicability to the business process setting we target with the DCDS model.…”

Section: Related Workmentioning

confidence: 99%

Verification of relational data-centric dynamic systems with external services

Hariri

Calvanese

Giacomo

et al. 2013

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

114

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Data-centric dynamic systems are systems where both the process controlling the dynamics and the manipulation of data are equally central. We study verification of (first-order) µ-calculus variants over relational data-centric dynamic systems, where data are maintained in a relational database, and the process is described in terms of atomic actions that evolve the database. Action execution may involve calls to external services, thus inserting fresh data into the system. As a result such systems are infinite-state. We show that verification is undecidable in general, and we isolate notable cases where decidability is achieved. Specifically we start by considering service calls that return values deterministically (depending only on passed parameters). We show that in a µ-calculus variant that preserves knowledge of objects appeared along a run we get decidability under the assumption that the fresh data introduced along a run are bounded, though they might not be bounded in the overall system. In fact we tie such a result to a notion related to weak acyclicity studied in data exchange. Then, we move to nondeterministic services and we investigate decidability under the assumption that knowledge of objects is preserved only if they are continuously present. We show that if infinitely many values occur in a run but do not accumulate in the same state, then we get again decidability. We give syntactic conditions to avoid this accumulation through the novel notion of "generate-recall acyclicity", which ensures that every service call activation generates new values that cannot be accumulated indefinitely.

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Section: Related Workmentioning

confidence: 99%

Verification of relational data-centric dynamic systems with external services

Hariri

Calvanese

Giacomo

et al. 2013

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

114

View full text Add to dashboard Cite

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“…Another open question is whether nonemptiness of safety forward alternating tree automata with 1 register [Jurdziński and Lazić 2007] is primitive recursive.…”

Section: Discussionmentioning

confidence: 99%

Safety alternating automata on data words

Lazić

2011

ACM Trans. Comput. Logic

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A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are considered, their nonemptiness is shown ExpSpace-complete, and their inclusion decidable but not primitive recursive. The same complexity bounds are obtained for satisfiability and refinement, respectively, for the safety fragment of linear temporal logic with freeze quantification. Dropping the safety restriction, adding past temporal operators, or adding one more register, each causes undecidability.

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“…This can be done in several ways, and with such encodings, the data equality relation becomes the equality between subterms. Therefore, this could be worth studying in order to relate our results on TAGC to decidability results on automata or logics on data trees like those in [28], [22].…”

Section: Discussionmentioning

confidence: 99%

The Emptiness Problem for Tree Automata with Global Constraints

Barguno

Creus

Godoy

et al. 2010

2010 25th Annual IEEE Symposium on Logic in Computer Science

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Abstract-We define tree automata with global constraints (TAGC), generalizing the class of tree automata with global equality and disequality constraints [1] (TAGED). TAGC can test for equality and disequality between subterms whose positions are defined by the states reached during a computation. In particular, TAGC can check that all the subterms reaching a given state are distinct. This constraint is related to monadic key constraints for XML documents, meaning that every two distinct positions of a given type have different values.We prove decidability of the emptiness problem for TAGC. This solves, in particular, the open question of decidability of emptiness for TAGED. We further extend our result by allowing global arithmetic constraints for counting the number of occurrences of some state or the number of different subterms reaching some state during a computation. We also allow local equality and disequality tests between sibling positions and the extension to unranked ordered trees. As a consequence of our results for TAGC, we prove the decidability of a fragment of the monadic second order logic on trees extended with predicates for equality and disequality between subtrees, and cardinality.

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Alternation-free modal mu-calculus for data trees

Abstract: An alternation-free modal µ-calculus over data trees is introduced and studied. A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element ("datum")

Cited by 39 publications

References 29 publications

Verification of relational data-centric dynamic systems with external services

Verification of relational data-centric dynamic systems with external services

Safety alternating automata on data words

The Emptiness Problem for Tree Automata with Global Constraints

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