The set E of strings is said to be definable (strongly definable) if there is a context-free grammar G such that E is the set of all terminal strings generated from the initial symbol (from all non­ terminal symbols) of G. The classification of definable and strongly definable sets in dependence on minimal number of nonterminal symbols needed for their generation is given.

We propose a new type of regulation on the derivation of a context-free grammar: the productions used for passing from a level of a derivation tree to the next level should have the right-hand members of the same length. We prove that such length synchronized context-free grammars characterize the family of ET0L languages, and therefore are equivalent with the synchronization context-free gramm...

We investigate the problem of training probabilistic context-free grammars on the basis of a distribution defined over an infinite set of trees, by minimizing the cross-entropy. This problem can be seen as a generalization of the well-known maximum likelihood estimator on (finite) tree banks. We prove an unexpected theoretical property of grammars that are trained in this way, namely, we show t...

Context awareness is increasingly gaining applicability in interactive ubiquitous mobile computing systems. Each context-aware application has its own set of behaviors to react to context modifications. This paper is concerned with the context modeling and the development methodology for context-aware systems. We proposed a rule-based approach and use the adaption tree to model the adaption rul...

We introduce a new concept of regular expression and context-free grammar for picture languages (sets of matrices over a nite alphabet) and compare and connect these two formalisms.

We establish that several classical context-free languages are inherently ambiguous by proving that their counting generating functions, when considered as analytic functions, exhibit some characteristic form of transcendental behaviour. To that purpose, we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages. ...

The fastest known algorithm for checking bisimulation equivalence of normed context-free processes worked in O(n) time. We give an alternative algorithm working in O(npolylog n) time, As a side effect we improve the best known upper bound for testing equivalence of simple context-free grammars from O(npolylog n) to O(npolylog n).

In papers [2] and [3] four criteria of complexity of context-free grammars (CFG's), denoted by Var, Lev, Lev„, and Depth, have been studied. These criteria reflect the intrinsic complexity of CFG's and they induce the criteria of complexity of contextfree languages (CFL's) which reflect the intrinsic complexity of the description of CFL's by CFG's. The criterion Prod (G) = the number of rules o...

This paper describes the Omphalos Context-Free Grammar Learning Competition held as part of the International Colloquium on Grammatical Inference 2004. The competition was created in an effort to promote the development of new and better grammatical inference algorithms for context-free languages, to provide a forum for the comparison of different grammatical inference algorithms and to gain in...

We use context free languages to analyze solution sets to one variable equations over free groups.