Abstract
The main contribution of the paper is a PTIME decision procedure for the satisfiability problem in a class of first-order Horn clauses. Our result is an extension of the tractable classes of Horn clauses of Basin & Ganzinger in several respects. For instance, our clauses may contain atomic formulas S ⊢ t where ⊢ is a predicate symbol and S is a finite set of terms instead of a term. ⊢ is used to represent any possible computation of an attacker, given a set of messages S. The class of clauses that we consider encompasses the clauses designed by Bana & Comon-Lundh for security proofs of protocols in a computational model.
Because of the (variadic) ⊢ predicate symbol, we cannot use ordered resolution strategies only, as in Basin & Ganzinger: given S ⊢ t, we must avoid computing S′ ⊢ t for all subsets S′ of S. Instead, we design PTIME entailment procedures for increasingly expressive fragments, such procedures being used as oracles for the next fragment.
Finally, we obtain a PTIME procedure for arbitrary ground clauses and saturated Horn clauses (as in Basin & Ganzinger), together with a particular class of (non saturated) Horn clauses with the ⊢ predicate and constraints (which are necessary to cover the application).
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Comon-Lundh, H., Cortier, V., Scerri, G. (2013). Tractable Inference Systems: An Extension with a Deducibility Predicate. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_6
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DOI: https://doi.org/10.1007/978-3-642-38574-2_6
Publisher Name: Springer, Berlin, Heidelberg
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