378 research outputs found
A regularity test for pushdown machines
It is possible to test a deterministic pushdown machine to determine if the language it recognizes is regular
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
Multi-Head Finite Automata: Characterizations, Concepts and Open Problems
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg,
1966). Since that time, a vast literature on computational and descriptional
complexity issues on multi-head finite automata documenting the importance of
these devices has been developed. Although multi-head finite automata are a
simple concept, their computational behavior can be already very complex and
leads to undecidable or even non-semi-decidable problems on these devices such
as, for example, emptiness, finiteness, universality, equivalence, etc. These
strong negative results trigger the study of subclasses and alternative
characterizations of multi-head finite automata for a better understanding of
the nature of non-recursive trade-offs and, thus, the borderline between
decidable and undecidable problems. In the present paper, we tour a fragment of
this literature
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
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