By Olaf Burkart

A universal procedure in software program engineering is to use throughout the layout section numerous based recommendations like top-down layout, decomposition and abstraction, whereas simply for this reason, within the implementation part, is the layout established to make sure reliability. yet this procedure neglects that imperative features of software program layout and software improvement have a robust formal personality which admits instrument aid for the development of trustworthy and proper computers in keeping with formal reasoning. This monograph presents a lot details either for theoreticians drawn to algebraic theories, and for software program engineers construction virtually appropriate instruments. the writer provides the theoretical foundations wanted for the verification of reactive, sequential infinite-state structures. new algorithms are brought bearing in mind automated verification of vital elements similar to protection or liveness properites of a given infinite-state procedure. The formal framework constructed comprises fresh effects from numerous theoretical components like technique algebras, fixpoint conception, modal logics and version checking.

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**Additional info for Automatic Verification of Sequential Infinite-State Processes**

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The norm of a process p, written as ||p||, is the length of the shortest transition sequence from p to a terminating state. If a process p cannot reach a terminating state its norm is defined to be infinite. A process is said to be normed if its norm is finite, and is called strongly normed if any successor a is normed. Finally, a transition p → p of a normed process p is called a norm-reducing transition if ||p || = ||p|| − 1. 22 2. e. we have p∼q implies ||p|| = ||q||. A different property associated with processes concerns the notion of determinism.

7 (Norm). The norm of a process p, written as ||p||, is the length of the shortest transition sequence from p to a terminating state. If a process p cannot reach a terminating state its norm is defined to be infinite. A process is said to be normed if its norm is finite, and is called strongly normed if any successor a is normed. Finally, a transition p → p of a normed process p is called a norm-reducing transition if ||p || = ||p|| − 1. 22 2. e. we have p∼q implies ||p|| = ||q||. A different property associated with processes concerns the notion of determinism.

3 (Operational Semantics). The operational semantics of a guarded BPA specification (V, Act, E, X1 ) is given by the labelled transition graph (V ∗ , Act, →) rooted at X1 where the transition relation → is given by the action relations for BPA on V ∗ × V ∗ . The process defined by X1 is then also called context-free. It can be shown that in this graph model any guarded BPA specification has a unique solution up to bisimulation equivalence [BK84]. Furthermore, for ease of presentation, it is useful that we can restrict our attention to BPA specifications in a certain normal form.