Order-sorted parameterization and induction
Semantics and algebraic specification
Constructors, sufficient completeness, and deadlock freedom of rewrite theories
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Proving safety properties of rewrite theories
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Tool interoperability in the Maude formal environment
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Towards a Maude formal environment
Formal modeling
Coverset induction with partiality and subsorts: a powerlist case study
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Order-Sorted equality enrichments modulo axioms
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
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This work develops new automated reasoning techniques for verifying the correctness of equationally specified programs These techniques are not just theoretical, but have been implemented, and applied to actual program verification projects. Although the work spans several different areas, a major theme of this work is to develop better techniques at the boundary between decidable and undecidable problems. That is, this work seeks out not just positive decidability results, but ways to extend the underlying techniques to be effective on problems outside of decidable subclasses. For program verification to succeed, we feel that two important directions must be pursued: (1) considering more expressive logics to allow designers to more easily specify systems, and (2) develop decision procedures that can reason efficiently about these more sophsticated logics. This work pursues both directions, and the main topics addressed include: new decidability and undecidability results for equational tree automata (Chapter 3), order-sorted unification (Chapter 4), sufficient completeness for specifications with partiality and rewriting modulo axioms (Chapter 5), completeness problems for context-sensitive specifications (Chapter 6), coverset induction in membership equational logic (Chapter 7), and a case study for verifying properties of powerlists with the Maude ITP (Chapter 8). Each of these theoretical topics have lead to the development of new libraries and tools. Two of the tools have already been used in external projects including our tree automata library's integration into the ACTAS protocol verification tool [126], and the order-sorted unification procedures use in the Maude-NRL protocol analyzer [49].