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The logic of equality with uninterpreted functions (EUF) provides a means of abstracting the manipulation of data by a processor when verifying the correctness of its control logic. By reducing formulas in this logic to propositional formulas, we can apply Boolean methods such as Ordered Binary Decision Diagrams (BDDs) and Boolean satisfiability checkers to perform the verification. We can exploit characteristics of the formulas describing the verification conditions to greatly simplify the propositional formulas generated. In particular, we exploit the property that many equations appear only in positive form. We can therefore reduce the set of interpretations of the function symbols that must be considered to prove that a formula is universally valid to those that are ``maximally diverse. We present experimental results demonstrating the efficiency of this approach when verifying pipelined processors using the method proposed by Burch and Dill.
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagners counting hierarchy, but also th
The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound $B$, a PDL formula $varphi$ and a CFM $mathcal{C}$, whether every existent
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER and FaCT++,
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely used in pro
In the present paper we consider the simplest non-classical extension $GL4$ of the well-known propositional provability logic $GL$ together with the notion of expressibility of formulas in a logic proposed by A. V. Kuznetsov. Conditions for expressib