The Complexity of Checking Non-Emptiness in Symbolic Tree Automata

2023/11/09 by Rodrigo Raya, Raya, Rodrigo
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2311.05250

openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of the accepted words. We use our decomposition to obtain tight computational complexity bounds on the decision problem for this automata class and an extension that considers linear arithmetic constraints on the underlying effective Boolean algebra

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