Efficient Solution of Language Equations Using Partitioned Representations

A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix closed, and are naturally represented by multi-level networks with latches. For this special case, we present an efficient computation, using partitioned representations, of the most general prefix-closed solution of the above class of language equations. The transition and the output relations of the FSMs for F and S in their partitioned form are represented by the sets of output and next state functions of the corresponding networks. Experimentally, we show that using partitioned representations is much faster than using monolithic representations, as well as applicable to larger problem instances.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

PROGRESSIVE SOLUTIONS TO FSM EQUATIONS

Abstract. The equation solving problem is to derive the behavior of the unknown component X knowing the joint behavior of the other components (or the context) C and the specification of the overall system S. The component X can be derived by solving the Finite State Machine (FSM) equation C ◊ X ∼ S, where ◊ is the parallel composition operator and ∼ is the trace equivalence or the trace reduction relation. A solution X to an FSM equation is called progressive if for every external input sequence the composition C ◊ X does not fall into a livelock without an exit. In this paper, we formally define the notion of a progressive solution to a parallel FSM equation and present an algorithm that derives a largest progressive solution (if a progressive solution exists). In addition, we generalize the work to a system of FSM equations. Application examples are provided

A new algorithm to solve synchronous FSM equations

Many problems over discrete event systems can be reduced to solving a synchronous FSM inequality A & X <= S or a synchronous FSM equation A & X = S, where X is a free variable and & is the synchronous composition operator. In this paper we address the problem of solving a multi-component FSM equation, We study the most general solution of a synchronous FSM equation defined over several FSMs. In particular, we show that a solvable equation has always a largest solution, then we consider the largest alphabet of actions over which a solution exists, from which it is possible to extract the largest solution over a restricted set of alphabets

Solving Parallel Equations with BALM-II

In this report we describe how to solve parallel language equations over regular languages / automata and finite state machines (FSMs), using the software package BALM-II. The original version of BALM could solve equations only with respect to synchronous composition; we extended the original code to solve also equations with respect to parallel composition, adding new commands and procedures. The new version of BALM is called BALM-II, of which this document provides a user's manual. Finally, as an important application, we describe how to synthesize protocol converters with BALM-II

Sedimentology and provenance of the Dunnottar and Crawton Groups, Lower Old Red Sandstone, Kincardineshire, Scotland

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