Abstract
A transformation is presented which converts any pushdown automaton (PDA)M 0 withn 0 states andp 0 stack symbols into an equivalent PDAM withn states and ⌈n 0 /n⌉2 p 0 stack symbols into an equivalent ofn, 1⩽n<n 0. This transformation preserves realtime behavior but not derterminism. The transformation is proved to be the best possible one in the following sense: for each choice of the parametersn 0 + 1 stack symbols for any desired value realtime PDAM 0 such that any equivalent PDAM (whether realtime or not) havingn states must have at least ⌈(n 0 /n)2 p0⌉ stack symbols. Furthermore, the loss of deterministic behavior cannot be avoided, since for each choice ofn 0 andp 0, there is a deterministic PDAM 0 such that no equivalent PDAM with fewer states can be deterministic.
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This research was supported in part by the National Science Foundation under Grants MCS76-10076 and MCS76-10076A01.
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Goldstine, J., Price, J.K. & Wotschke, D. On reducing the number of states in a PDA. Math. Systems Theory 15, 315–321 (1981). https://doi.org/10.1007/BF01786988
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DOI: https://doi.org/10.1007/BF01786988