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In this paper a platform is presented, that given a stochastic context-free grammar (SCFG), automatically outputs the description of the parser in synthesizable hardware description language (HDL) which can be downloaded in an Field Programmable Gate Arrays (FPGA) board. Initially, according to our methodology the SCFG is augmented with attributes which store the probability values and can be evaluated through corresponding stack actions. The architecture of the produced system is based on a proposed extension of Earley's parallel algorithm, which given an input string, generates the parse trees in the form of an AND-Or parse tree. This AND-or parse tree is then traversed using a proposed tree traversal technique in order to execute the corresponding actions in the correct order, so as to compute the necessary probabilities. The platform is suitable for embedded systems applications where a natural language interface is required or in pattern recognition tasks. The parser generated by the presented platform has been tested for various SCFGs and compared to software approaches. The performance comparison is one to two orders of magnitude in favor of the presented hardware, compared to previous software approaches, depending on the application, the input string length and the number of produced trees. [ABSTRACT FROM AUTHOR]

Hairpin completion is a formal operation inspired from DNA biochemistry. It is known that the (one step) hairpin completion of a regular language is linear context-free, but not regular in general. Further, it is decidable whether the (one step) hairpin completion of a regular language is regular. However, it is an open question whether the iterated hairpin completion of a regular language is regular, even if it is a singleton. If the word is a non-crossing α-word, there are results, but for crossing words there are no results. In this paper, we give necessary and sufficient conditions that the iterated hairpin completion of a given crossing (2, 2)-α-word in is regular. [ABSTRACT FROM AUTHOR]

This paper deals with insertability and mainly extractablity of codes. A code C is called insertable (or extractable) if the free submonoid C* generated by C satisfies if z, implies (or z, implies ). We show that a finite insertable code is a full uniform code. On the other hand there are many finite extractable codes which are not full uniform codes. We cannot still characterize the structures of infinite extractable codes. Here we give some results on the class of infix extractable codes. First, we consider a necessary and sufficient condition whether a given infix code C is extractable or not by using the syntactic graph of the code. Secondly, we investigate the extractability for the families of other related bifix codes. We newly define the bifix codes, called e(m)-codes and -codes, and refer to the extractability of them. [ABSTRACT FROM AUTHOR]