Minimization of AND-EXOR expressions using rewrite rules
Conditions for generating optimal two-level AND-EXOR representations using rewrite rules are considered. Four results are presented. First, it is shown that a necessary condition for obtaining minimality is a temporary increase in the size of expressions during minimization. Second, a sufficient con...
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| Veröffentlicht in: | IEEE Trans. Comput Jg. 42; H. 5; S. 568 - 576 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
IEEE
01.05.1993
Institute of Electrical and Electronics Engineers (IEEE) Institute of Electrical and Electronics Engineers |
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| ISSN: | 0018-9340 |
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| Abstract | Conditions for generating optimal two-level AND-EXOR representations using rewrite rules are considered. Four results are presented. First, it is shown that a necessary condition for obtaining minimality is a temporary increase in the size of expressions during minimization. Second, a sufficient condition for obtaining minimality that consists of adding certain two rules to rule sets proposed in the literature is given. Third, transformations that allow the minimization of an expression to proceed by minimizing a transformed expression instead are defined. Fourth, it is determined experimentally that the above three theoretical results lead to better benchmarks results as well.< > |
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| AbstractList | Conditions for generating optimal two-level AND-EXOR representations using rewrite rules are considered. Four results are presented. First, it is shown that a necessary condition for obtaining minimality is a temporary increase in the size of expressions during minimization. Second, a sufficient condition for obtaining minimality that consists of adding certain two rules to rule sets proposed in the literature is given. Third, transformations that allow the minimization of an expression to proceed by minimizing a transformed expression instead are defined. Fourth, it is determined experimentally that the above three theoretical results lead to better benchmarks results as well.< > Conditions for generating optimal two-level AND-EXOR representations using rewrite rules are considered. Four results are presented. First, it is shown that a necessary condition for obtaining minimality is a temporary increase in the size of expressions during minimization. Second, a sufficient condition for obtaining minimality that consists of adding certain two rules to rule sets proposed in the literature is given. Third, transformations that allow the minimization of an expression to proceed by minimizing a transformed expression instead are defined. Fourth, it is determined experimentally that the above three theoretical results lead to better benchmarks results as well |
| Author | Brand, D. Sasao, T. |
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| Cites_doi | 10.1109/TC.1979.1675308 10.1109/ISMVL.1990.122597 10.2307/2307285 10.1007/978-1-4615-3154-8_12 10.1109/ICCD.1990.130257 10.1007/978-1-4613-2821-6 10.1109/12.45212 10.1109/TC.1987.1676890 10.1109/PGEC.1967.264777 10.1109/T-C.1970.222878 10.1109/T-C.1972.223475 10.1109/TC.1982.1676087 10.1109/TC.1984.1676349 10.1147/rd.185.0443 10.1049/ip-e.1983.0045 10.1109/ISMVL.1991.130742 10.1109/TC.1979.1675401 10.1109/IREPGELC.1954.6499441 |
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| Keywords | Red-Muller expansion Nondeterministic algorithm Logic minimization Rewriting Programming Two level representation Rewrite rull Programming theory |
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| References | ref12 muroga (ref13) 1979 ref15 ref14 fujiwara (ref8) 1986 ref11 ref10 davio (ref5) 1978 ref1 ref17 brayton (ref2) 1982 ref16 ref19 ref18 sasao (ref22) 1990 ref23 brayton (ref3) 1984 ref25 ref20 ref21 helliwel (ref9) 1988 brand (ref4) 1991 ref7 sasao (ref24) 1993 ref6 |
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| Snippet | Conditions for generating optimal two-level AND-EXOR representations using rewrite rules are considered. Four results are presented. First, it is shown that a... |
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| SubjectTerms | Applied sciences Circuit testing Computer science Computer science; control theory; systems Exact sciences and technology Logic Minimization methods Modules (abstract algebra) Programming theory Sufficient conditions Theoretical computing |
| Title | Minimization of AND-EXOR expressions using rewrite rules |
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