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Satisfiability of Context-Free String Constraints with Subword-Ordering and Transducers

Authors C. Aiswarya , Soumodev Mal , Prakash Saivasan

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ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • satisfiability
  • subword
  • string constraints
  • context-free
  • transducers

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Abstract

We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their transductions. The satisfiability problem is known to be undecidable even without rational transductions. It is known to be NExptime-complete without transductions, if the subword relations between variables do not have a cyclic dependency between them. We show that the satisfiability problem stays decidable in this fragment even when rational transductions are added. It is 2NExptime-complete with context-free membership, and NExptime-complete with only regular membership. For the lower bound we prove a technical lemma that is of independent interest: The length of the shortest word in the intersection of a pushdown automaton (of size 𝒪(n)) and n finite-state automata (each of size 𝒪(n)) can be double exponential in n.

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C. Aiswarya, Soumodev Mal, and Prakash Saivasan. Satisfiability of Context-Free String Constraints with Subword-Ordering and Transducers. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.STACS.2024.5

Author Details

C. Aiswarya
  • Chennai Mathematical Institute, India
  • CNRS, ReLaX, IRL 2000, Chennai, India
Soumodev Mal
  • Chennai Mathematical Institute, India
Prakash Saivasan
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
  • CNRS, ReLaX, IRL 2000, Chennai, India

Funding

  • Saivasan, Prakash: MATRICS GRANT (MTR/2022/000312).

Acknowledgements

We thank Paul Gastin for helpful discussions.

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