Word Equations in the Context of String Solving

Day, Joel D.

doi:10.1007/978-3-031-05578-2_2

Cited by 1 publication

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“…In such attacks, the attacker constructs an input string in such a way that the underlying semantics of the interpretation is changed. The CSPS, and more importantly its implementations in solvers [38,1,16,36,37,25,35] have provided the much needed power to model and verify programs for such vulnerabilities. This in turn has directed the study to explore the boundaries of solvability.…”

Section: Introductionmentioning

confidence: 99%

On the Satisfiability of Context-free String Constraints with Subword-Ordering

Aiswarya

Mal

Prakash

2022

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science

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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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