Abstract.
This paper investigates the logic-automata-connection for Duration Calculus. It has been frequently observed that Duration Calculus with linear duration terms comes close to being a logic of linear hybrid automata. We attempt to make this relation precise by constructing Kleene-connection between duration-constrained regular expressions and a subclass of linear hybrid automata called loop-reset automata in which any variable tested in a loop is reset in the same loop. The formalism of duration-constrained regular expressions is an extension of regular expressions with duration constraints, which are essentially formulas of Duration Calculus without negation, yet extended by a Kleene-star operator. In this paper, we show that this formalism is equivalent in expressive power to loop-reset automata by providing a translation procedure from expressions to automata and vice verse.
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Received June 1999
Accepted in revised form September 2003 by M. R. Hansen and C. B. Jones
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Xuandong, L., Jianhua, Z., Tao, Z. et al. Duration-constrained regular expressions. Formal Aspects of Computing 16, 155–163 (2004). https://doi.org/10.1007/s00165-004-0033-x
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DOI: https://doi.org/10.1007/s00165-004-0033-x