1,357 research outputs found
Weak Alternating Timed Automata
Alternating timed automata on infinite words are considered. The main result
is a characterization of acceptance conditions for which the emptiness problem
for these automata is decidable. This result implies new decidability results
for fragments of timed temporal logics. It is also shown that, unlike for MITL,
the characterisation remains the same even if no punctual constraints are
allowed
Boundedness in languages of infinite words
We define a new class of languages of -words, strictly extending
-regular languages.
One way to present this new class is by a type of regular expressions. The
new expressions are an extension of -regular expressions where two new
variants of the Kleene star are added: and . These new
exponents are used to say that parts of the input word have bounded size, and
that parts of the input can have arbitrarily large sizes, respectively. For
instance, the expression represents the language of infinite
words over the letters where there is a common bound on the number of
consecutive letters . The expression represents a similar
language, but this time the distance between consecutive 's is required to
tend toward the infinite.
We develop a theory for these languages, with a focus on decidability and
closure. We define an equivalent automaton model, extending B\"uchi automata.
The main technical result is a complementation lemma that works for languages
where only one type of exponent---either or ---is used.
We use the closure and decidability results to obtain partial decidability
results for the logic MSOLB, a logic obtained by extending monadic second-order
logic with new quantifiers that speak about the size of sets
Counter Machines and Distributed Automata: A Story about Exchanging Space and Time
We prove the equivalence of two classes of counter machines and one class of
distributed automata. Our counter machines operate on finite words, which they
read from left to right while incrementing or decrementing a fixed number of
counters. The two classes differ in the extra features they offer: one allows
to copy counter values, whereas the other allows to compute copyless sums of
counters. Our distributed automata, on the other hand, operate on directed path
graphs that represent words. All nodes of a path synchronously execute the same
finite-state machine, whose state diagram must be acyclic except for
self-loops, and each node receives as input the state of its direct
predecessor. These devices form a subclass of linear-time one-way cellular
automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the
proceedings of AUTOMATA 2018
Remarks on Parikh-recognizable omega-languages
Several variants of Parikh automata on infinite words were recently
introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants
coincides with blind counter machine as introduced by Fernau and Stiebe
[Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every
-language recognized by a blind counter machine is of the form
for Parikh recognizable languages , but
blind counter machines fall short of characterizing this class of
-languages. They posed as an open problem to find a suitable
automata-based characterization. We introduce several additional variants of
Parikh automata on infinite words that yield automata characterizations of
classes of -language of the form for all
combinations of languages being regular or Parikh-recognizable. When
both and are regular, this coincides with B\"uchi's classical
theorem. We study the effect of -transitions in all variants of
Parikh automata and show that almost all of them admit
-elimination. Finally we study the classical decision problems
with applications to model checking.Comment: arXiv admin note: text overlap with arXiv:2302.04087,
arXiv:2301.0896
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
On the Path-Width of Integer Linear Programming
We consider the feasibility problem of integer linear programming (ILP). We
show that solutions of any ILP instance can be naturally represented by an
FO-definable class of graphs. For each solution there may be many graphs
representing it. However, one of these graphs is of path-width at most 2n,
where n is the number of variables in the instance. Since FO is decidable on
graphs of bounded path- width, we obtain an alternative decidability result for
ILP. The technique we use underlines a common principle to prove decidability
which has previously been employed for automata with auxiliary storage. We also
show how this new result links to automata theory and program verification.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Integer Vector Addition Systems with States
This paper studies reachability, coverability and inclusion problems for
Integer Vector Addition Systems with States (ZVASS) and extensions and
restrictions thereof. A ZVASS comprises a finite-state controller with a finite
number of counters ranging over the integers. Although it is folklore that
reachability in ZVASS is NP-complete, it turns out that despite their
naturalness, from a complexity point of view this class has received little
attention in the literature. We fill this gap by providing an in-depth analysis
of the computational complexity of the aforementioned decision problems. Most
interestingly, it turns out that while the addition of reset operations to
ordinary VASS leads to undecidability and Ackermann-hardness of reachability
and coverability, respectively, they can be added to ZVASS while retaining
NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
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