Unambiguous Constrained Automata

Cadilhac, Michaël; Finkel, Alain; McKenzie, Pierre

doi:10.1007/978-3-642-31653-1_22

Cited by 8 publications

(17 citation statements)

References 10 publications

(7 reference statements)

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“…The author would like to thank Thomas Finn Lidbetter (University of Waterloo) for telling me this topic. The author also thank to an anonymous reviewer for letting me know some known results on unambiguous CA [10] and pointing out that the decidability results presented in this note are also from those results.…”

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confidence: 87%

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Note on the Infiniteness and Equivalence Problems for Word-MIX Languages

Sin'ya

2018

Preprint

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In this note we provide a (decidable) graph-structural characterisation of the infiniteness of L(w1, . . . , w k ), where L(w1, . . . ,set of all words that contain the same number of subword occurrences of parameter words w1, . . . , w k . We also provide the decidable characterisation of the equivalence for those languages. Although those two decidability results are also obtained from more general known decidability results on unambiguous constrained automata, this note tries to give a self-contained (without the knowledge about constrained automata) proof of the decidability.

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confidence: 87%

“…. , w k ) is always recognised by a deterministic CA, and its regularity and Parikh image are effectively computable [10]. In this note, we provide a self-contained (without the knowledge about constrained automata) description of a decidable, necessary and sufficient condition for the infiniteness of L(5w 1 , .…”

Section: Introductionmentioning

confidence: 99%

Note on the Infiniteness and Equivalence Problems for Word-MIX Languages

Sin'ya

2018

Preprint

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“…Since the class of 2DPA is equivalent to the class of UPA that is known to be closed under Boolean operations [3,17], we get the closure properties of 2DPA for free, although with non-optimal complexity. We show here that they can be realised in linear-time for intersection and union, and with linear state-complexity for the complement.…”

Section: Closure Properties and Comparison Problemsmentioning

confidence: 99%

Two-way Parikh Automata

Filiot,

Guha,

Mazzocchi

2019

Preprint

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Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer theory, as they enjoy decidable emptiness problem.In this paper, we study two-way Parikh automata. We show that emptiness becomes undecidable in the non-deterministic case. However, it is PSpace-C when the number of visits to any input position is bounded and the semi-linear set is given as an existential Presburger formula. We also give tight complexity bounds for the inclusion, equivalence and universality problems. Finally, we characterise precisely the complexity of those problems when the semi-linear constraint is given by an arbitrary Presburger formula.1 E. Filiot is a research associate of F.R.S.-FNRS. He is supported by the ARC Project Transform Fédération Wallonie-Bruxelles and the FNRS CDR project J013116F. 2 S. Guha is supported by the ARC project "Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond" ( Fédération Wallonie-Bruxelles) 3 N Mazzocchi is a PhD student funded by a FRIA fellowship from the F.R.S.-FNRS.

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“…Theorems 15 and 16 together provide a characterization of those pairs of unambiguous two-way transducers T 1 , T 2 for which there is a bounded regular resynchronizer R such that T 1 ⊆ o R(T 2 ). The effectiveness of this characterization stems from the decidability of regularity of languages recognized by unambiguous Parikh automata [CFM13]. This result requires unambiguity and uses Presburger arithmetics to determine for each (simple) loop a threshold such that iterating the loop more than the threshold always satisfies the Parikh constraint.…”

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confidence: 99%

On Synthesis of Resynchronizers for Transducers

Bose,

Krishna,

Muscholl

et al. 2019

Preprint

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We study two formalisms that allow to compare transducers over words under origin semantics: rational and regular resynchronizers, and show that the former are captured by the latter. We then consider some instances of the following synthesis problem: given transducers T1, T2, construct a rational (resp. regular) resynchronizer R, if it exists, such that T1 is contained in R(T2) under the origin semantics. We show that synthesis of rational resynchronizers is decidable for functional, and even finite-valued, one-way transducers, and undecidable for relational one-way transducers. In the two-way setting, synthesis of regular resynchronizers is shown to be decidable for unambiguous two-way transducers. For larger classes of two-way transducers, the decidability status is open.

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Unambiguous Constrained Automata

Cited by 8 publications

References 10 publications

Note on the Infiniteness and Equivalence Problems for Word-MIX Languages

Note on the Infiniteness and Equivalence Problems for Word-MIX Languages

Two-way Parikh Automata

On Synthesis of Resynchronizers for Transducers

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