WQO Dichotomy for 3-Graphs

Lasota, Sławomir; Piórkowski, Radoslaw

doi:10.1007/978-3-319-89366-2_30

Cited by 4 publications

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References 24 publications

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“…The proof was suggested by Lasota and Piórkowski [12]. It is analogous to proof of [5, Theorem 17], except two-counter machines are replaced by reset VASS-es; used encoding of reset VASS into register transducer is similar to [4, Example 3].…”

Section: ▶ Theorem 19 Zeroness Of Polynomial Grammars With One Substi...mentioning

confidence: 99%

On polynomial grammars extended with substitution

Schmude¹

2021

Preprint

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We investigate decidability of equivalence of register transducers, also called copyful Streaming String Transducers in case of string input, extended with an operation of substituting a register for all occurrences of a given letter in another register. We reduce to zeroness of polynomial grammars (over ring of polynomials) extended with analogous substitution operation by encoding strings into polynomials; a similar method was used successfully by Seidl et al. in 2018. We give two restrictions under which register transducers with substitution have decidable equivalence. They seem to be very restrictive but on the other hand, they seem to be on the edge of the scope of this "polynomial" method, as in the third result we give a rather restricted model of polynomial grammars with substitution that has undecidable equivalence.

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Section: ▶ Theorem 19 Zeroness Of Polynomial Grammars With One Substi...mentioning

confidence: 99%

On polynomial grammars extended with substitution

Schmude¹

2021

Preprint

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WQO Dichotomy for 3-Graphs

Lasota

Piórkowski

2018

Lecture Notes in Computer Science

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Abstract. We investigate data-enriched models, like Petri nets with data, where executability of a transition is conditioned by a relation between data values involved. Decidability status of various decision problems in such models may depend on the structure of data domain. According to the WQO Dichotomy Conjecture, if a data domain is homogeneous then it either exhibits a well quasi-order (in which case decidability follows by standard arguments), or essentially all the decision problems are undecidable for Petri nets over that data domain.We confirm the conjecture for data domains being 3-graphs (graphs with 2-colored edges). On the technical level, this results is a significant step beyond known classification results for homogeneous structures.

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WQO dichotomy for 3-graphs

Lasota

Piórkowski

2020

Information and Computation

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WQO Dichotomy for 3-Graphs

Cited by 4 publications

References 24 publications

On polynomial grammars extended with substitution

On polynomial grammars extended with substitution

WQO Dichotomy for 3-Graphs

WQO dichotomy for 3-graphs

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