First Order Alternation

Abstract: We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted predicate terms. The model is closed under union, intersection and complement, and its emptiness problem is undecidable, even for the simplest data theory of equality. To cope with this limitation, we develop an abstraction refinement semi-algorithm based on lazy annotation of the symbolic execution paths with interpolants, obtained by applying (i) quantifier elimination with witness term generation and (ii) Lyndon interpolation in the quantifier-free data theory with uninterpreted predicate symbols. This provides a method for checking inclusion of timed and finite-memory register automata, and emptiness of quantified predicate automata, previously used in the verification of parameterized concurrent programs, composed of replicated threads, with a shared-memory communication model.