Michal P. Chytil

Serial Composition of 2-Way Finite-State Transducers and Simple Programs on Strings

Hopcroft and Ullman ~i] described an algorithm for reverse run of deterministic generalized sequential machines. This algorithm does not go beyond abilities of 2-way finite automata. The algorithm was then used [ 2 ] in the proof of the fact that serial composition of a deterministic gsm A 1 and a 2way deterministic finite-state transducer A 2 can be replaced by a single 2-way deterministic finite-state transducer, say A 3. Let us recall the main idea of the proof (c.f. fig. i).

On the parallel recognition of ambiguous context-free languages

Abstract We present a simple parallel algorithm recognizing unambiguous context-free languages on a CREW PRAM in time log 2 n with only n 3 processors. This gives the smallest number of processors known for the recognition of unambiguous context-free languages in polylogarithmic time. Using the same framework a new algorithm is also given for the recognition of deterministic context-free languages in log 2 n time with quadratic number of processors.

Caterpillars and context-free languages

We use the concept of a caterpillar tree to study the properties of context-free languages, in particular new results about the index of context-free languages and the recognition of context-free languages are obtained this way. The first group of results points to differences between ambiguous and unambiguous languages. For unambiguous languages we prove the existence of a gap between finite index and O(log n) index. For ambiguous languages there is no such a gap: we prove the existence of grammars with infinite but arbitrarily slowly growing index. We show that bounded languages are of finite index and give a deterministic log space algorithm for the recognition of deterministic finite index languages. We also describe a parallel algorithm recognizing deterministic context-free languages on a CREW-PRAM with O(n2) processors in time O(log2n).

Kins of context-free languages

We study languages which can be described as limits of fast converging infinite sequences of context-free languages. Such a sequence \(L_0 \subseteq L_1 \subseteq L_2 \subseteq\) ... is fast converging if each string w of its limit language belongs to an Li which has a grammatical description very concise in comparison with the length of w . We prove that these languages are closely related to context-free languages in several properties: pumping lemma, interchange lemma, regularity of unary languages, full AFL properties. The languages can differ, however, in their computational complexity: we construct languages of arbitrarily high complexity, even languages which are not recursively enumerable, but have fast context-free approximations.

Panic Mode without Panic

We introduce a method for the automatic construction of error correcting parsers and the notion of skeletal set of a language constitutive for the method. The method is studied completely in the framework of formal language theory.

Cycle Chain Code Picture Languages

A picture word is a string over the alphabet {u, d, l, r}. These symbols mean drawing of a unit line in direction up, down, left, and right, respectively. A picture word describes a walk in the plane; its trace is the picture it describes. A set of picture words describes a (chain code) picture language.

Categorial grammars for strata of non-CF languages and their parsers

We introduce a generalization of categorial grammar extending its descriptive power, and a simple model of categorial grammar parser. Both tools can be adjusted to particular strata of languages via restricting grammatical or computational complexity.