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2 Fundamenta Informaticae

2 2004

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A Polynomial-Time Algorithm for Checking Consistency of Free-Choice Signal Transition Graphs

100%

Esparza J.

Fundamenta Informaticae

2004

tom Vol. 62, nr 2

197--220

Signal Transition Graphs (STGs) are one of the most popular models for the specification of asynchronous circuits. A STG can be implemented if it admits a so-called consistent and complete binary encoding. Deciding this is EXPSPACE-hard for arbitrary STGs, and so a lot of attention has been devoted to the subclass of free-choice STGs, which offers a good compromise between expressive power and analizability. In the last years, polynomial time synthesis techniques have been developed for free-choice STGs, but they assume that the STG has a consistent binary encoding. This paper presents the first polynomial algorithm for checking consistency.

Detecting State Encoding Conflicts in STG Unfoldings Using SAT

63%

Khomenko V. , Koutny M. , Yakovlev A.

Fundamenta Informaticae

2004

tom Vol. 62, nr 2

221--241

The behaviour of asynchronous circuits is often described by Signal Transition Graphs (STGs), which are Petri nets whose transitions are interpreted as rising and falling edges of signals. One of the crucial problems in the synthesis of such circuits is that of identifying whether an STG satisfies the Complete State Coding (CSC) requirement (which states that semantically different reachable states must have different binary encodings), and, if necessary, modifying the STG (by, e.g., inserting new signals helping to trace the current state) to meet this requirement. This is usually done using reachability graphs. In this paper, we avoid constructing the reachability graph of an STG, which can lead to state space explosion, and instead use only the information about causality and structural conflicts between the events involved in a finite and complete prefix of its unfolding. We propose an efficient algorithm for detection of CSC conflicts based on the Boolean Satisfiability (SAT) approach. Following the basic formulation of the state encoding conflict relationship, we present some problem-specific optimization rules. Experimental results show that this technique leads not only to huge memory savings when compared to the CSC conflicts detection methods based on reachability graphs, but also to significant speedups in many cases.