A data link protocol developed and used by Philips Electronics is modeled and veri ed using I/O automata theory. Correctness is computer-checked with the Coq proof development s y s t e m .

This chapter addresses the question how to verify distributed and communicating systems in an effective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras. The first step towards such verifications is to extend process algebra (ACP) with equational data types which adds required expressive power to describe distributed systems. Subsequently, linear process operators, invariants, the cones and foci method, the composition of many similar parallel processes, and the use of confluence are explained, as means to verify increasingly complex systems. As illustration, verifications of the serial line interface protocol (SLIP) and the IEEE 1394 tree identify protocol are included.

This chapter addresses the question how to verify distributed and communicating systems in an effective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras. The first step towards such verifications is to extend process algebra (ACP) with equational data types which adds required expressive power to describe distributed systems. Subsequently, linear process operators, invariants, the cones and foci method, the composition of many similar parallel processes, and the use of confluence are explained, as means to verify increasingly complex systems. As illustration, verifications of the serial line interface protocol (SLIP) and the IEEE 1394 tree identify protocol are included.

We provide several notions for confluence in processes and we show how these relate to r-inertness, i.e. ifs __:_-c. s', then s and s' are equivalent. Using clustered linear processes we show how these notions can conveniently be used to reduce the size of state spaces and simplify the structure of processes while preserving equivalence.

In this paper we study automatic veri cation of proofs in process algebra. Formulas of process algebra are represented by t ypes in typed-calculus. Inhabitants (terms) of these types represent proofs. The speci c typed-calculus we use is the Calculus of Inductive Constructions as implemented in the interactive p r o o f construction program COQ. Axiom A1. Assumes (alt x y)=(alt y x). Axiom A2. Assumes (alt x (alt y z))=(alt (alt x y) z). Axiom A3. Assumes x=(alt x x). Axiom A4. Assumes (alt (seq x z) (seq y z))=(seq (alt x y) z). Axiom A5. Assumes (seq x (seq y z))=(seq (seq x y) z). Axiom A6. Assumes x=(alt x Delta). Axiom A7. Assumes Delta=(seq Delta x). Axiom CM1. Assumes (alt (alt (Lmer x y) (Lmer y x)) (comm x y))= (mer x y). Axiom CM2. Assumes (seq (ia D a d) x)=(Lmer (ia D a d) x). Axiom CM3. Assumes (seq (ia D a d) (mer x y))= (Lmer (seq (ia D a d) x) y). Axiom CM4. Assumes (alt (Lmer x z) (Lmer y z))=(Lmer (alt x y) z). Axiom CM5. Assumes (seq(comm (ia D a d) (ia E b e)) x)= (comm (seq (ia D a d) x) (ia E b e)). Axiom CM6. Assumes (seq (comm (ia D a d) (ia E b e)) x)= (comm (ia D a d) (seq (ia E b e) x)). Axiom CM7. Assumes (seq (comm (ia D a d) (ia E b e)) (mer x y))= (comm (seq (ia D a d) x) (seq (ia E b e) y)). Axiom CM8. Assumes (alt (comm x z) (comm y z))=(comm (alt x y) z). Axiom CM9. Assumes (alt (comm x y) (comm x z))=(comm x (alt y z)). Axiom D1. Assumes ((In ehlist a L))->(ia D a d)= (enc L (ia D a d)). Axiom D2. Assumes (In ehlist a L)->Delta=(enc L (ia D a d)). Axiom D3. Assumes (alt (enc L x) (enc L y))=(enc L (alt x y)). Axiom D4. Assumes (seq (enc L x) (enc L y))=(enc L (seq x y)). End ACP.