335 research outputs found
Partially ordered two-way Büchi automata
We introduce partially ordered two-way Büchi automata over infinite words. As for finite words, the nondeterministic variant recognizes the fragment Sigma2 of first-order logic FO[<] and the deterministic version yields the Delta2-definable omega-languages. As a byproduct of our results, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations.
In addition, we have coNP-completeness results for the emptiness problem and the inclusion problem over deterministic partially ordered two-way Büchi automata
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
Wadge Degrees of -Languages of Petri Nets
We prove that -languages of (non-deterministic) Petri nets and
-languages of (non-deterministic) Turing machines have the same
topological complexity: the Borel and Wadge hierarchies of the class of
-languages of (non-deterministic) Petri nets are equal to the Borel and
Wadge hierarchies of the class of -languages of (non-deterministic)
Turing machines which also form the class of effective analytic sets. In
particular, for each non-null recursive ordinal there exist some -complete and some -complete -languages of Petri nets, and the supremum of
the set of Borel ranks of -languages of Petri nets is the ordinal
, which is strictly greater than the first non-recursive ordinal
. We also prove that there are some -complete, hence non-Borel, -languages of Petri nets, and
that it is consistent with ZFC that there exist some -languages of
Petri nets which are neither Borel nor -complete. This
answers the question of the topological complexity of -languages of
(non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326
Determinising Parity Automata
Parity word automata and their determinisation play an important role in
automata and game theory. We discuss a determinisation procedure for
nondeterministic parity automata through deterministic Rabin to deterministic
parity automata. We prove that the intermediate determinisation to Rabin
automata is optimal. We show that the resulting determinisation to parity
automata is optimal up to a small constant. Moreover, the lower bound refers to
the more liberal Streett acceptance. We thus show that determinisation to
Streett would not lead to better bounds than determinisation to parity. As a
side-result, this optimality extends to the determinisation of B\"uchi
automata
B\"uchi VASS recognise w-languages that are Sigma^1_1 - complete
This short note exhibits an example of a Sigma^1_1-complete language that can
be recognised by a one blind counter B\"uchi automaton (or equivalently a
B\"uchi VASS with only one place)
A Component-oriented Framework for Autonomous Agents
The design of a complex system warrants a compositional methodology, i.e.,
composing simple components to obtain a larger system that exhibits their
collective behavior in a meaningful way. We propose an automaton-based paradigm
for compositional design of such systems where an action is accompanied by one
or more preferences. At run-time, these preferences provide a natural fallback
mechanism for the component, while at design-time they can be used to reason
about the behavior of the component in an uncertain physical world. Using
structures that tell us how to compose preferences and actions, we can compose
formal representations of individual components or agents to obtain a
representation of the composed system. We extend Linear Temporal Logic with two
unary connectives that reflect the compositional structure of the actions, and
show how it can be used to diagnose undesired behavior by tracing the
falsification of a specification back to one or more culpable components
Permutation Games for the Weakly Aconjunctive -Calculus
We introduce a natural notion of limit-deterministic parity automata and
present a method that uses such automata to construct satisfiability games for
the weakly aconjunctive fragment of the -calculus. To this end we devise a
method that determinizes limit-deterministic parity automata of size with
priorities through limit-deterministic B\"uchi automata to deterministic
parity automata of size and with
priorities. The construction relies on limit-determinism to avoid the full
complexity of the Safra/Piterman-construction by using partial permutations of
states in place of Safra-Trees. By showing that limit-deterministic parity
automata can be used to recognize unsuccessful branches in pre-tableaux for the
weakly aconjunctive -calculus, we obtain satisfiability games of size
with priorities for weakly aconjunctive
input formulas of size and alternation-depth . A prototypical
implementation that employs a tableau-based global caching algorithm to solve
these games on-the-fly shows promising initial results
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