From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527

Parametrized Stochastic Grammars for RNA Secondary Structure Prediction

We propose a two-level stochastic context-free grammar (SCFG) architecture for parametrized stochastic modeling of a family of RNA sequences, including their secondary structure. A stochastic model of this type can be used for maximum a posteriori estimation of the secondary structure of any new sequence in the family. The proposed SCFG architecture models RNA subsequences comprising paired bases as stochastically weighted Dyck-language words, i.e., as weighted balanced-parenthesis expressions. The length of each run of unpaired bases, forming a loop or a bulge, is taken to have a phase-type distribution: that of the hitting time in a finite-state Markov chain. Without loss of generality, each such Markov chain can be taken to have a bounded complexity. The scheme yields an overall family SCFG with a manageable number of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications Workshop (ITA 2007

Sanakielet ja lokaalisuus

In this master's thesis we study the generalization of word languages into multi-dimensional arrays of letters i.e picture languages. Our main interest is the class of recognizable picture languages which has many properties in common with the robust class of regular word languages. After surveying the basic properties of picture languages, we present a logical characterization of recognizable picture languages—a generalization of Büchi's theorem of word languages into pictures, namely that the class of recognizable picture languages is the one recognized by existential monadic second-order logic. The proof presented is a recent one that makes the relation between tilings and logic clear in the proof. By way of the proof we also study the locality of the model theory of picture structures through logical locality obtained by normalization of EMSO on those structures. A continuing theme in the work is also to compare automata and recognizability between word and picture languages. In the fourth section we briefly look at topics related to computativity and computational complexity of recognizable picture languages