By Olaf Burkart
A universal procedure in software program engineering is to use throughout the layout section numerous established ideas like top-down layout, decomposition and abstraction, whereas purely hence, within the implementation part, is the layout verified to make sure reliability. yet this process neglects that valuable points of software program layout and application improvement have a robust formal personality which admits device aid for the development of trustworthy and proper computers according to formal reasoning. This monograph presents a lot details either for theoreticians attracted to algebraic theories, and for software program engineers construction essentially proper instruments. the writer offers the theoretical foundations wanted for the verification of reactive, sequential infinite-state platforms. new algorithms are brought taking into account computerized verification of significant features akin to security or liveness properites of a given infinite-state process. The formal framework built includes contemporary effects from a variety of theoretical components like strategy algebras, fixpoint idea, modal logics and version checking.
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Additional resources for Automatic Verification of Sequential Infinite-State Processes
In fact, all recently obtained algorithms for deciding bisimulation equivalence for normed BPA processes [Cau90, Gro91, HS91, HT94, HM94] rely on this reduction. Finally, we mention that in the presence of unnormed processes we only have the following trivial right-cancellation rule. 3 (Right-cancellation rule for unnormed BPA). If X is unnormed, then αXβ ∼ αX. 3 Self-bisimulations In order to prove bisimilarity of two processes p and q it suffices to exhibit a bisimulation relating p and q. However, since this task is sometimes difficult to accomplish another proof technique introduced by Caucal [Cau90] is often useful.
To range over elements in V ∗ . For technical convenience, we use to denote the empty variable sequence with the convention α = α = α. Moreover, the function | . | gives the length of a sequence. Finally, we shall often give a BPA specification by simply presenting E with the convention that the first variable represents the root. 2 Normedness In the sequel we shall distinguish normed and unnormed BPA specifications. As usual, a BPA specification is said to be normed if all variables are normed and it is called unnormed otherwise.
Usually, proofs benefit most from the existence of normal forms as they can often significantly be simplified if the device at hand can be assumed to be of a specific form. In formal language theory, for example, Chomsky Normal Form, as well as Greibach Normal Form, both constitute important normal forms for contextfree grammars. Furthermore, for pushdown automata a normal form is known which admits to restrict the attention to pushdown automata pushing at most 2 symbols onto the stack when reading an input symbol4 .