Equisolvability of series vs. controller's topology in synchronous language equations
Yevtushenko, N.
Villa, T.
Brayton, R.K.
Petrenko, A.
Sangiovanni-Vincentelli, A.L.
Dept. of Electr. Eng. & Comput. Sci., Tomsk State Univ., Russia;
This paper appears in: Design, Automation and Test in Europe Conference and Exhibition, 2003
Publication Date: 3-7 March 2003
On page(s): 1154- 1155
ISSN: 1530-1591
ISBN: 0-7695-1870-2
INSPEC Accession Number: 7831276
Digital Object Identifier: 10.1109/DATE.2003.1253778
Current Version Published: 2003-12-19
Abstract
Given a plant MA and a specification MC, the largest solution of the FSM equation MX · MA ≤ MC contains all possible discrete controllers MX. Often we are interested in computing the complete solutions whose composition with the plant is exactly equivalent to the specification. Not every solution contained in the largest one satisfies such property, that holds instead for the complete solutions of the series topology. We study the relation between the solvability of an equation for the series topology and of the corresponding equation for the controller's topology. We establish that, if MA is a deterministic FSM, then the FSM equation MX · MA ≤ MC is solvable for the series topology with an unknown head component iff it is solvable for the controller's topology. Our proof is constructive, i.e., for a given solution MB of the series topology it shows how to build a solution MD of the controller's topology and vice versa.
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