# Alternative proof procedures for finite-state machines in higher-order logic

## Abstract

Verification of digital circuits in higher-order logic often requires the proof of temporal propositional logic formulae. The implementation of decision procedures for this logic or finite-state machines is however not very easy within the HOL system, since it requires the proof of certain fixpoint theorems and a creation of a new theory based on it. The main contribution of this paper is to give some alternative proof procedures so that proof tactics can be developed for directly solving these goals. These proof procedures can be classified into two categories. Firstly, a set of easily implementable proof methods which do not use knowledge of fixpoint theorems are given. Since these methods are incomplete, the second category exploits an external program for computing fixpoint lemmata which can then be easily proved in HOL.

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