Deciding Regularity of the Set of Instances of a Set of Terms with Regular Constraints is EXPTIME-Complete

Authors:
Omer Giménez;Guillem Godoy;Sebastian Maneth
Affiliations:
ogimenez@lsi.upc.edu and ggodoy@lsi.upc.edu;-;sebastian.maneth@nicta.com.au
Venue:
SIAM Journal on Computing
Year:
2011

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Abstract

Finite-state tree automata are a well-studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is restricted to instantiations of a regular set given by a tree automaton. The problem was recently proved decidable, but with an unknown complexity. Here, the exact complexity of the problem is determined by proving EXPTIME-completeness. The main contribution is a new, exponential time algorithm that performs various exponential transformations on the involved terms and tree automata and decides regularity by analyzing formulas over inequation and height predicates.