Abstract
Security protocols employing cryptographic primitives with algebraic properties are conveniently modeled using Horn clauses modulo equational theories. We consider clauses corresponding to the class \(\mathcal{H}3\) of Nielson, Nielson and Seidl. We show that modulo the theory ACU of an associative-commutative symbol with unit, as well as its variants like the theory XOR and the theory AG of Abelian groups, unsatisfiability is NP-complete. Also membership and intersection-non-emptiness problems for the closely related class of one-way as well as two-way tree automata modulo these equational theories are NP-complete. A key technical tool is a linear time construction of an existential Presburger formula corresponding to the Parikh image of a context-free language. Our algorithms require deterministic polynomial time using an oracle for existential Presburger formulas, suggesting efficient implementations are possible.
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Verma, K.N., Seidl, H., Schwentick, T. (2005). On the Complexity of Equational Horn Clauses. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_25
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DOI: https://doi.org/10.1007/11532231_25
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