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Discovering grammar of an unknown text as an optimisation problem

Ryszawa P. A.

Computer Science and Mathematical Modelling

2017

No. 6

15--22

This paper concerns the problem of discovering an unknown grammar from a text sample. The discovering methods are formulated as optimisation problems based on a binary representation of context-sensitive grammars. The representation starts with a longest possible vector of bits to, finally, make it more compact so as to be usable in practical applications. For the sake of simplicity, considered are only noncontracting (length-preserving) grammars of order 2, excluding productions of the form P: A→ B and those deriving the empty string, i.e P: A → ε.

Niniejszy artykuł dotyczy problemu odkrywania nieznanej gramatyki z próbki tekstu. Metody odkrywania zostały sformułowane jako zadania optymalizacyjne oparte na binarnej reprezentacji gramatyk kontekstowych. Reprezentacja ta, początkowo jako najdłuższy możliwy wektor bitów, ostatecznie została skrócona do zwięzłej postaci, nadającej się do wykorzystania praktycznego. Dla uproszczenia uwzględniono tylko gramatyki nieskracające rzędu 2, z wyłączeniem produkcji postaci P: A→ B i tych wyprowadzających łańcuch pusty, tj. P: A → ε.

Non-renewal multistate system with Semi-Markov components

Grabski F.

Journal of Polish Safety and Reliability Association

2014

Vol. 5, No. 1

63--70

The paper deals with non-renewal multistate monotone systems consisting of multistate components which are modeled by the semi-Markov processes. In the case of a non-renewal system the multistate reliability functions of the system components and the whole system are discussed. All presented concepts and models are illustrated by simple numerical examples.

New formula for the failure/repair frequency of multi-state monotone systems and its applications

Korczak E.

Control and Cybernetics

2007

Vol. 36, no 1

219-239

The paper deals with calculation methods for failure and repair frequencies of multi-state monotone systems, both for the instantaneous and steady state cases. First, the fixed demand is considered. Based on the binary representation of multi-state structure, we have obtained a new formula for the failure/repair frequency. This formula is used to derive simple rules for the calculation of failure/repair frequency. These rules show how to convert an expression for the system availability into appropriate expression for the system failure/repair frequency. The applicability of the rules is illustrated by some examples. Finally, expressions for the failure/repair frequency for systems operating under random demand are obtained. Since both input and output data have similar format, the rules can be used in a recursive manner, allowing easy analysis of complex systems with hierarchical structure.