Formal Theory of Basic COSY
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In every expression as described above, the semicolon specifies sequential occurrences of the events named or subexpressions, and comma specifies a mutually exclusive occurrence of one of the events named or subexpressions. The comma binds more strongly than the semicolon, so that the expression “a;b, c” means “first event a must occur, after which exclusively either event b or event c must occur”. An expression may be enclosed in conventional parentheses with Kleene star appended, as for instance “(d, e)*” which means that the enclosed specification applies zero or more times. In other words, an expression between path and end may be understood as an ordinary regular expression. The only difference is that “∪” is replaced by “,”, concatenation is replaced by “;”, and mutually exclusive choice binds more strongly than concatenation1. Thus for instance “a; b, c” is equivalent to “a(b ∪ c)” in the traditional notation for regular expressions. Moreover, by definition, the parentheses path and end correspond to “(” and “)*” respectively, so that a single path specifies repeated (or cyclic) sequences of event occurrences.
KeywordsPartial Order Formal Theory Regular Expression Vector Sequence Firing Sequence
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