9,081 research outputs found
Computational Complexity of Synchronization under Regular Commutative Constraints
Here we study the computational complexity of the constrained synchronization
problem for the class of regular commutative constraint languages. Utilizing a
vector representation of regular commutative constraint languages, we give a
full classification of the computational complexity of the constraint
synchronization problem. Depending on the constraint language, our problem
becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition,
we derive a polynomial time decision procedure for the complexity of the
constraint synchronization problem, given some constraint automaton accepting a
commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and
Combinatorics Conference); 2nd version is update of the published version and
1st version; both contain a minor error, the assumption of maximality in the
NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of
incomparability of the vectors in main theorem; fixed in this version. See
(new) discussion after main theore
Synchronizing weighted automata
We introduce two generalizations of synchronizability to automata with
transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently,
to finite sets of matrices in K^nxn.) Let us call a matrix A
location-synchronizing if there exists a column in A consisting of nonzero
entries such that all the other columns of A are filled by zeros. If
additionally all the entries of this designated column are the same, we call A
synchronizing. Note that these notions coincide for stochastic matrices and
also in the Boolean semiring. A set M of matrices in K^nxn is called
(location-)synchronizing if M generates a matrix subsemigroup containing a
(location-)synchronizing matrix. The K-(location-)synchronizability problem is
the following: given a finite set M of nxn matrices with entries in K, is it
(location-)synchronizing?
Both problems are PSPACE-hard for any nontrivial semiring. We give sufficient
conditions for the semiring K when the problems are PSPACE-complete and show
several undecidability results as well, e.g. synchronizability is undecidable
if 1 has infinite order in (K,+,0) or when the free semigroup on two generators
can be embedded into (K,*,1).Comment: In Proceedings AFL 2014, arXiv:1405.527
Visibly Pushdown Modular Games
Games on recursive game graphs can be used to reason about the control flow
of sequential programs with recursion. In games over recursive game graphs, the
most natural notion of strategy is the modular strategy, i.e., a strategy that
is local to a module and is oblivious to previous module invocations, and thus
does not depend on the context of invocation. In this work, we study for the
first time modular strategies with respect to winning conditions that can be
expressed by a pushdown automaton.
We show that such games are undecidable in general, and become decidable for
visibly pushdown automata specifications.
Our solution relies on a reduction to modular games with finite-state
automata winning conditions, which are known in the literature.
We carefully characterize the computational complexity of the considered
decision problem. In particular, we show that modular games with a universal
Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and
when the winning condition is given by a CARET or NWTL temporal logic formula
the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple
fragments of these logics.
As a further contribution, we present a different solution for modular games
with finite-state automata winning condition that runs faster than known
solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Real-Time Vector Automata
We study the computational power of real-time finite automata that have been
augmented with a vector of dimension k, and programmed to multiply this vector
at each step by an appropriately selected matrix. Only one entry
of the vector can be tested for equality to 1 at any time. Classes of languages
recognized by deterministic, nondeterministic, and "blind" versions of these
machines are studied and compared with each other, and the associated classes
for multicounter automata, automata with multiplication, and generalized finite
automata.Comment: 14 page
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
Revisiting the Equivalence Problem for Finite Multitape Automata
The decidability of determining equivalence of deterministic multitape
automata (or transducers) was a longstanding open problem until it was resolved
by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability
yields a co_NP upper bound, but apparently not much more is known about the
complexity of the problem. In this paper we give an alternative proof of
decidability, which follows the basic strategy of Harju and Karhumaki but
replaces their use of group theory with results on matrix algebras. From our
proof we obtain a simple randomised algorithm for deciding language equivalence
of deterministic multitape automata and, more generally, multiplicity
equivalence of nondeterministic multitape automata. The algorithm involves only
matrix exponentiation and runs in polynomial time for each fixed number of
tapes. If the two input automata are inequivalent then the algorithm outputs a
word on which they differ
Bounded Counter Languages
We show that deterministic finite automata equipped with two-way heads
are equivalent to deterministic machines with a single two-way input head and
linearly bounded counters if the accepted language is strictly bounded,
i.e., a subset of for a fixed sequence of symbols . Then we investigate linear speed-up for counter machines. Lower
and upper time bounds for concrete recognition problems are shown, implying
that in general linear speed-up does not hold for counter machines. For bounded
languages we develop a technique for speeding up computations by any constant
factor at the expense of adding a fixed number of counters
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