Crossing the Syntactic Barrier: Hom-Disequalities for \({\mathcal H}_1\)-Clauses

  • Andreas Reuß
  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)


We extend \({\mathcal H}_1\)-clauses with disequalities between images of terms under a tree homomorphism (hom-disequalities). This extension allows to test whether two terms are distinct modulo a semantic interpretation, allowing, e.g., to neglect information that is not considered relevant for the intended comparison. We prove that \({\mathcal H}_1\)-clauses with hom-disequalities are more expressive than \({\mathcal H}_1\)-clauses with ordinary term disequalities, and that they are incomparable with \({\mathcal H}_1\)-clauses with disequalities between paths. Our main result is that \({\mathcal H}_1\)-clauses with this new type of constraints can be normalized into an equivalent tree automaton with hom-disequalities. Since emptiness for that class of automata turns out to be decidable, we conclude that satisfiability is decidable for positive Boolean combinations of queries to predicates defined by \({\mathcal H}_1\)-clauses with hom-disequalities.


Horn Clause Cryptographic Protocol Ground Term Tree Automaton Unary Predicate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Reuß
    • 1
  • Helmut Seidl
    • 1
  1. 1.Technische Universität MünchenGermany

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