736 research outputs found
On shuffle products, acyclic automata and piecewise-testable languages
We show that the shuffle L \unicode{x29E2} F of a piecewise-testable
language and a finite language is piecewise-testable. The proof relies
on a classic but little-used automata-theoretic characterization of
piecewise-testable languages. We also discuss some mild generalizations of the
main result, and provide bounds on the piecewise complexity of L
\unicode{x29E2} F
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
Separability by Short Subsequences and Subwords
The separability problem for regular languages asks, given two regular languages I and E, whether there exists a language S that separates the two, that is, includes I but contains nothing from E. Typically, S comes from a simple, less expressive class of languages than I and E. In general, a simple separator can be seen as an approximation of I or as an explanation of how I and E are different. In a database context, separators can be used for explaining the result of regular path queries or for finding explanations for the difference between paths in a graph database, that is, how paths from given nodes u_1 to v_1 are different from those from u_2 to v_2. We study the complexity of separability of regular languages by combinations of subsequences or subwords of a given length k. The rationale is that the parameter k can be used to influence the size and simplicity of the separator. The emphasis of our study is on tracing the tractability of the problem
Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages
The purpose of this paper is to provide efficient algorithms that decide
membership for classes of several Boolean hierarchies for which efficiency (or
even decidability) were previously not known. We develop new forbidden-chain
characterizations for the single levels of these hierarchies and obtain the
following results: - The classes of the Boolean hierarchy over level
of the dot-depth hierarchy are decidable in (previously only the
decidability was known). The same remains true if predicates mod for fixed
are allowed. - If modular predicates for arbitrary are allowed, then
the classes of the Boolean hierarchy over level are decidable. - For
the restricted case of a two-letter alphabet, the classes of the Boolean
hierarchy over level of the Straubing-Th\'erien hierarchy are
decidable in . This is the first decidability result for this hierarchy. -
The membership problems for all mentioned Boolean-hierarchy classes are
logspace many-one hard for . - The membership problems for quasi-aperiodic
languages and for -quasi-aperiodic languages are logspace many-one complete
for
- …