Automatic Verification of Sequential Infinite-State by Olaf Burkart PDF

By Olaf Burkart

ISBN-10: 3540639829

ISBN-13: 9783540639824

A universal strategy in software program engineering is to use in the course of the layout part quite a few dependent thoughts like top-down layout, decomposition and abstraction, whereas in basic terms for that reason, within the implementation part, is the layout verified to make sure reliability. yet this process neglects that imperative points of software program layout and application improvement have a powerful formal personality which admits software aid for the development of trustworthy and proper computers in keeping with formal reasoning. This monograph offers a lot info either for theoreticians drawn to algebraic theories, and for software program engineers construction virtually correct instruments. the writer offers the theoretical foundations wanted for the verification of reactive, sequential infinite-state structures. new algorithms are brought bearing in mind automated verification of significant elements resembling protection or liveness properites of a given infinite-state process. The formal framework constructed consists of fresh effects from a number of theoretical parts like strategy algebras, fixpoint concept, modal logics and version checking.

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Additional info for Automatic Verification of Sequential Infinite-State Processes

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The introduction of fragments in combination with the n-ary sequential composition causes now a problem which was not present in the BPA case: when combining processes we have to take care of the arity or type of an expression. Formally, given a set of control states Q = { q1 , . . 1. A PDPA expression is then said to be well-typed if its arity is defined. An immediate consequence of our definition is that well-typed PDPA expressions have either arity 1 or n determining the type of sequential composition to use for them.

Xn }, – a finite set of actions or terminals Act, – a finite set of recursive process equations E = { Xi =df Ei | 1 ≤ i ≤ n }, where each Ei is a BPAδε expression with free variables in V , – a variable X1 ∈ V , called the root. 4 A BPAδε specification is the process theory analogon to a context-free grammar in formal language theory. 26 2. Background If V , and Act are clear from the context we will occasionally present a specification merely by its equations where we adopt the convention that the first variable represents the root.

Qn , Xm ), γ]). X is a right-hand side summand of X in ER . Therefore we also have [q, Zγ] a X → [q , β]; [¯ qn , γ] X and clearly ¯ m , γ] ∼ [(q , X ), βγ] S [q , βγ] qn × X [(q , X ), β]; [¯ ∼ [q , β]; [¯ qn , γ] X X. As the converse direction is shown by symmetric arguments this concludes the proof. 1. If the PDPA specification D is in k-PDNF the resulting expanded PDPA specification D constructed in the previous proof is also in k-PDNF. Proof. Since the construction of the expanded PDPA specification only deals with integrating the regular process structure into the control component of the given PDPA specification, it is easy to see that the length of the words in the stack component does not change.

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Automatic Verification of Sequential Infinite-State Processes by Olaf Burkart

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