3,799 research outputs found
Partially Ordered Two-way B\"uchi Automata
We introduce partially ordered two-way B\"uchi automata and characterize
their expressive power in terms of fragments of first-order logic FO[<].
Partially ordered two-way B\"uchi automata are B\"uchi automata which can
change the direction in which the input is processed with the constraint that
whenever a state is left, it is never re-entered again. Nondeterministic
partially ordered two-way B\"uchi automata coincide with the first-order
fragment Sigma2. Our main contribution is that deterministic partially ordered
two-way B\"uchi automata are expressively complete for the first-order fragment
Delta2. As an intermediate step, we show that deterministic partially ordered
two-way B\"uchi automata are effectively closed under Boolean operations.
A small model property yields coNP-completeness of the emptiness problem and
the inclusion problem for deterministic partially ordered two-way B\"uchi
automata.Comment: The results of this paper were presented at CIAA 2010; University of
Stuttgart, Computer Scienc
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps from the free monoid into the field of real numbers
with a rational domain. We show that two families of such series are actually
the same: the unambiguous rational series on the one hand, and the max-plus and
min-plus rational series on the other hand. The decidability of equality was
known to hold in both families with different proofs, so the above unifies the
picture. We give an effective procedure to build an unambiguous automaton from
a max-plus automaton and a min-plus one that recognize the same series
An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects
A zero-one language L is a regular language whose asymptotic probability
converges to either zero or one. In this case, we say that L obeys the zero-one
law. We prove that a regular language obeys the zero-one law if and only if its
syntactic monoid has a zero element, by means of Eilenberg's variety theoretic
approach. Our proof gives an effective automata characterisation of the
zero-one law for regular languages, and it leads to a linear time algorithm for
testing whether a given regular language is zero-one. In addition, we discuss
the logical aspects of the zero-one law for regular languages.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
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