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Summary: Decidable Classes of Inductive Theorems ?
Jurgen Giesl 1 and Deepak Kapur 2
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany,
giesl@informatik.rwth-aachen.de
2 Computer Science Dept., University of New Mexico, Albuquerque, NM 87131, USA
kapur@cs.unm.edu
Abstract. Kapur and Subramaniam [8] de ned syntactical classes of
equations where inductive validity is decidable. Thus, their validity can
be checked without any user interaction and hence, this allows an integra-
tion of (a restricted form of) induction in fully automated reasoning tools
such as model checkers. However, the results of [8] were only restricted
to equations. This paper extends the classes of conjectures considered in
[8] to a larger class of arbitrary quanti er-free formulas (e.g., conjectures
also containing negation, conjunction, disjunction, etc.).
1 Introduction
Inductive theorem provers usually require massive manual intervention and they
may waste huge amounts of time on proof attempts which fail due to the in-
completeness of the prover. Therefore, induction has not yet been integrated in
fully automated reasoning systems (i.e., model checkers) used for hardware and
protocol veri cation, static and type analyses, byte-code veri cation, and proof-
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