Helmut Seidl and Andreas Reuß. Extending H1-Clauses with Disequalities. Information Processing Letters, 111(20):1007-1013, 2011.
The class H1 has proven particularly useful for the analysis of term-manipulating programs such as cryptographic protocols. Here, we show that clauses from that class can be extended with disequalities between arbitrary terms while retaining decidability of satisfiability. The proof is based on a normalization procedure together with a procedure to decide whether a finite automaton with disequalities accepts less than k elements, and a subtle combinatorial argument to prove that only finitely many disequalities need to be considered.