427 research outputs found
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
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
Hairdressing in groups: a survey of combings and formal languages
A group is combable if it can be represented by a language of words
satisfying a fellow traveller property; an automatic group has a synchronous
combing which is a regular language. This article surveys results for combable
groups, in particular in the case where the combing is a formal language.Comment: 17 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTMon1/paper24.abs.htm
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)
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
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