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On the Complexity of Consistency and Complete State Coding for Signal Transition Graphs

Esparza J., Jančar P., Miller A.

Fundamenta Informaticae

2008

Vol. 86, nr 3

227-253

Signal Transition Graphs (STGs) are a popular formalism for the specification of asynchronous circuits. A necessary condition for the implementability of an STG is the existence of a consistent and complete state encoding. For an important subclass of STGs, the marked graph STGs, we show that checking consistency is polynomial, but checking the existence of a complete state coding is co-NP-complete. In fact, co-NP-completeness already holds for acyclic and 1-bounded marked graph STGs and for live and 1-bounded marked graph STGs. We add some relevant results for free-choice, bounded, and general STGs.

Detecting State Encoding Conflicts in STG Unfoldings Using SAT

Khomenko V., Koutny M., Yakovlev A.

Fundamenta Informaticae

2004

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.

A structural encoding technique for the synthesis of asynchronous circuits

Carmona J., Cortadella J., Pastor E.

Fundamenta Informaticae

2002

Vol. 50, nr 2

135-154

This paper presents a method for the automatic synthesis of asynchronous circuits from Petri net specifications. The method is based on a structural encoding of the system in such a way that a circuit implementation is always guaranteed. Moreover, a set of transformations is presented for the subclass of Free-Choice Petri nets that enables the exploration of different solutions. The set of transformations is derived from previous work on Petri net synthesis. Both the encoding technique and the set of transformations preserve the property of free-choiceness, thus enabling the use of structural methods for the synthesis of asynchronous circuits. Preliminary experimental results indicate that the quality of the circuits is comparable to that obtained by methods that require an exhaustive enumeration of the state space. This novel synthesis method opens the door to the synthesis of large control specifications generated from hardware description languages.