5,286 research outputs found
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
Remarks on separating words
The separating words problem asks for the size of the smallest DFA needed to
distinguish between two words of length <= n (by accepting one and rejecting
the other). In this paper we survey what is known and unknown about the
problem, consider some variations, and prove several new results
Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes
We study cooperating distributed grammar systems working in hybrid modes in
connection with the finite index restriction in two different ways: firstly, we
investigate cooperating distributed grammar systems working in hybrid modes
which characterize programmed grammars with the finite index restriction;
looking at the number of components of such systems, we obtain surprisingly
rich lattice structures for the inclusion relations between the corresponding
language families. Secondly, we impose the finite index restriction on
cooperating distributed grammar systems working in hybrid modes themselves,
which leads us to new characterizations of programmed grammars of finite index.Comment: In Proceedings AFL 2014, arXiv:1405.527
Controlled Bidirectional Grammars
We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages
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