Factorisation of finite state machines under strong and observational equivalences

Abstract

Abstract. The factorisation problem is to construct the specification of a submodule X when the specifications of the system and all submodules but X are given. It is usually described by the equation P [ X e Q where P and X are submodules of system Q, I is a composition operator, and & is the equivalence criterion. In this paper we use a finite state machine (FSM) model consistent with CCS and study two factorisation problems: P III X-Q and P III X ~ Q, where Ill is a derived CCS composition operator, -and ~ represent strong and observational equivalences. Algorithms are presented and proved correct to find the most general specification of submodule X for P III X -Q with Q r-deterministic and for P III X--~ Q with Q deterministic. Conditions on the submachines of the most general solutions that remain solutions to P III X Q (P I1[ X ~ Q) are given. This paper extends and is based on the work of M. W. Shields.

Modular Supervisory Control with Equivalence-Based Abstraction and Covering-Based Conflict Resolution

“…Subautomaton H of G is state observable in G with respect to the event set c if for all s and q ∈ δ h (q 0 , s), and all σ ∈ c , P τ (s)σ ∈ L(H) ⇒ δ h (q, σ ) = δ g (q, σ ) Taken together, state controllability and state observability provide that H represents a deterministic control law with respect to G. This is demonstrated formally by the following theorem that shows that a deterministic automaton H obs that generates and marks the same languages as H will produce a result that is bisimulation equivalent to H when it is composed with G. In essence, H obs can be considered a deterministic supervisor that achieves the specification represented by the nondeterministic automaton H for the nondeterministic plant model G. Similar results for generating control for bisimulation equivalence can be found in Qin and Lewis (1991), Madhusudan and Thiagarajan (2002) and Tabuada (2004), but none demonstrate the following specific result. Here we implicitly assume the states of the automata are reachable.…”

Solving asynchronous equations

“…In this context, a question arises how to design a component that combined with a known part of the system, called the context, satisfies a given overall specification. The problem is also known as the problem of submodule construction [Mer83], component redesign [Kimn] , [Rh091], [Wat93], controller design [Azi95], equation solving [Par89], [Lar90] , [Qin91], [Che96] or machine factorization [Qin9l]. This problem has many important applications, ranging from hardware optimization to protocol design.…”

Progressive Solutions to a Parallel Automata Equation

“…This work was later extended to the cases where the behavior of the components is described in CCS or CSP [8], by FSM [9,14] or input/output automata [11,6,3].…”