1,239 research outputs found
A Note on Limited Pushdown Alphabets in Stateless Deterministic Pushdown Automata
Recently, an infinite hierarchy of languages accepted by stateless
deterministic pushdown automata has been established based on the number of
pushdown symbols. However, the witness language for the n-th level of the
hierarchy is over an input alphabet with 2(n-1) elements. In this paper, we
improve this result by showing that a binary alphabet is sufficient to
establish this hierarchy. As a consequence of our construction, we solve the
open problem formulated by Meduna et al. Then we extend these results to
m-state realtime deterministic pushdown automata, for all m at least 1. The
existence of such a hierarchy for m-state deterministic pushdown automata is
left open
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
Marking Shortest Paths On Pushdown Graphs Does Not Preserve MSO Decidability
In this paper we consider pushdown graphs, i.e. infinite graphs that can be
described as transition graphs of deterministic real-time pushdown automata. We
consider the case where some vertices are designated as being final and we
built, in a breadth-first manner, a marking of edges that lead to such vertices
(i.e., for every vertex that can reach a final one, we mark all out-going edges
laying on some shortest path to a final vertex).
Our main result is that the edge-marked version of a pushdown graph may
itself no longer be a pushdown graph, as we prove that this enrich graph may
have an undecidable MSO theory.
In this paper we consider pushdown graphs, i.e. infinite graphs that can be
described as transition graphs of deterministic real-time pushdown automata. We
consider the case where some vertices are designated as being final and we
build, in a breadth-first manner, a marking of edges that lead to such vertices
(i.e., for every vertex that can reach a final one, we mark all out-going edges
laying on some shortest path to a final vertex).
Our main result is that the edge-marked version of a pushdown graph may
itself no longer be a pushdown graph, as we prove that the MSO theory of this
enriched graph may be undecidable.Comment: 11 pages, 2 figure
Model-Checking of Ordered Multi-Pushdown Automata
We address the verification problem of ordered multi-pushdown automata: A
multi-stack extension of pushdown automata that comes with a constraint on
stack transitions such that a pop can only be performed on the first non-empty
stack. First, we show that the emptiness problem for ordered multi-pushdown
automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown
automata, the set of all predecessors of a regular set of configurations is an
effectively constructible regular set. We exploit this result to solve the
global model-checking which consists in computing the set of all configurations
of an ordered multi-pushdown automaton that satisfy a given w-regular property
(expressible in linear-time temporal logics or the linear-time \mu-calculus).
As an immediate consequence, we obtain an 2ETIME upper bound for the
model-checking problem of w-regular properties for ordered multi-pushdown
automata (matching its lower-bound).Comment: 31 page
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