1,028 research outputs found
Computing downward closures for stacked counter automata
The downward closure of a language of words is the set of all (not
necessarily contiguous) subwords of members of . It is well known that the
downward closure of any language is regular. Although the downward closure
seems to be a promising abstraction, there are only few language classes for
which an automaton for the downward closure is known to be computable.
It is shown here that for stacked counter automata, the downward closure is
computable. Stacked counter automata are finite automata with a storage
mechanism obtained by \emph{adding blind counters} and \emph{building stacks}.
Hence, they generalize pushdown and blind counter automata.
The class of languages accepted by these automata are precisely those in the
hierarchy obtained from the context-free languages by alternating two closure
operators: imposing semilinear constraints and taking the algebraic extension.
The main tool for computing downward closures is the new concept of Parikh
annotations. As a second application of Parikh annotations, it is shown that
the hierarchy above is strict at every level.Comment: 34 pages, 1 figure; submitte
Monoid automata for displacement context-free languages
In 2007 Kambites presented an algebraic interpretation of
Chomsky-Schutzenberger theorem for context-free languages. We give an
interpretation of the corresponding theorem for the class of displacement
context-free languages which are equivalent to well-nested multiple
context-free languages. We also obtain a characterization of k-displacement
context-free languages in terms of monoid automata and show how such automata
can be simulated on two stacks. We introduce the simultaneous two-stack
automata and compare different variants of its definition. All the definitions
considered are shown to be equivalent basing on the geometric interpretation of
memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper
The Complexity of Downward Closure Comparisons
The downward closure of a language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of every language is regular. Moreover, recent results show that downward closures are computable for quite powerful system models.
One advantage of abstracting a language by its downward closure is that then equivalence and inclusion become decidable. In this work, we study the complexity of these two problems. More precisely, we consider the following decision problems: Given languages K and L from classes C and D, respectively, does the downward closure of K include (equal) that of L?
These problems are investigated for finite automata, one-counter automata, context-free grammars, and reversal-bounded counter automata. For each combination, we prove a completeness result either for fixed or for arbitrary alphabets. Moreover, for Petri net languages, we show that both problems are Ackermann-hard and for higher-order pushdown automata of order k, we prove hardness for complements of nondeterministic k-fold exponential time
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