1,295 research outputs found
On the Existence of Universal Finite or Pushdown Automata
We investigate the (non)-existence of universal automata for some classes of
automata, such as finite automata and pushdown automata, and in particular the
influence of the representation and encoding function. An alternative approach,
using transition systems, is presented too.Comment: In Proceedings DCM 2011, arXiv:1207.6821. Sadly, Manfred Kudlek
passed away June 18, 2012, before publication of this pape
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
Edit Distance for Pushdown Automata
The edit distance between two words is the minimal number of word
operations (letter insertions, deletions, and substitutions) necessary to
transform to . The edit distance generalizes to languages
, where the edit distance from to
is the minimal number such that for every word from
there exists a word in with edit distance at
most . We study the edit distance computation problem between pushdown
automata and their subclasses. The problem of computing edit distance to a
pushdown automaton is undecidable, and in practice, the interesting question is
to compute the edit distance from a pushdown automaton (the implementation, a
standard model for programs with recursion) to a regular language (the
specification). In this work, we present a complete picture of decidability and
complexity for the following problems: (1)~deciding whether, for a given
threshold , the edit distance from a pushdown automaton to a finite
automaton is at most , and (2)~deciding whether the edit distance from a
pushdown automaton to a finite automaton is finite.Comment: An extended version of a paper accepted to ICALP 2015 with the same
title. The paper has been accepted to the LMCS journa
Highly Undecidable Problems For Infinite Computations
We show that many classical decision problems about 1-counter
omega-languages, context free omega-languages, or infinitary rational
relations, are -complete, hence located at the second level of the
analytical hierarchy, and "highly undecidable". In particular, the universality
problem, the inclusion problem, the equivalence problem, the determinizability
problem, the complementability problem, and the unambiguity problem are all
-complete for context-free omega-languages or for infinitary rational
relations. Topological and arithmetical properties of 1-counter
omega-languages, context free omega-languages, or infinitary rational
relations, are also highly undecidable. These very surprising results provide
the first examples of highly undecidable problems about the behaviour of very
simple finite machines like 1-counter automata or 2-tape automata.Comment: to appear in RAIRO-Theoretical Informatics and Application
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
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
Pushdown Compression
The pressing need for eficient compression schemes for XML documents has
recently been focused on stack computation [6, 9], and in particular calls for
a formulation of information-lossless stack or pushdown compressors that allows
a formal analysis of their performance and a more ambitious use of the stack in
XML compression, where so far it is mainly connected to parsing mechanisms. In
this paper we introduce the model of pushdown compressor, based on pushdown
transducers that compute a single injective function while keeping the widest
generality regarding stack computation. The celebrated Lempel-Ziv algorithm
LZ78 [10] was introduced as a general purpose compression algorithm that
outperforms finite-state compressors on all sequences. We compare the
performance of the Lempel-Ziv algorithm with that of the pushdown compressors,
or compression algorithms that can be implemented with a pushdown transducer.
This comparison is made without any a priori assumption on the data's source
and considering the asymptotic compression ratio for infinite sequences. We
prove that Lempel-Ziv is incomparable with pushdown compressors
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