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arXiv · 2401.07996

Satisfiability of Context-free String Constraints with Subword-ordering and Transducers

C Aiswarya·Soumodev Mal·Prakash Saivasan
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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, Prakash Saivasan. 2024-01-15. Satisfiability of Context-free String Constraints with Subword-ordering and Transducers. https://arxiv.org/abs/2401.07996

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