Harry R. Lewis/Christos H. Papadimitriou: Elements of the Theory of Computation. London [et al.]: Prentice-Hall, 1981. ISBN 0-13-273426-5.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Of course, the present thesis neither is able to convey the mathematical theory behind finite state technologies, nor it is possible to sketch the multitude of its numerous applications in Linguistics, considering the sparse space restrictions. For the former, the reader might want to refer to [Lewis Papadimitriou, 1981], while [Kornai, 1997] with its references could serve as introduction to the latter. Nonetheless, the subsequent section intends to outline the rationale for which finite state methods were of great importance in Language Engineering, starting from the origins of the field up to the most recent ....

....be possible with a phrasestructure grammar. 7 An example for such a component would be a module which utilizes context free rules to filter out the output of a finite state transducer. Since the intersection of a context free language with a regular language is context free (a proof is given by [Lewis Papadimitriou, 1981], p. 121) the language recognized by this system would be context free. 2.1.4 Finite State Approximations of Context Free Grammars It already has been mentioned that the Patti system is based on finite state techniques. In this context, it might be of interest that several different algorithms ....

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Harry R. Lewis/Christos H. Papadimitriou: Elements of the Theory of Computation. London [et al.]: Prentice-Hall, 1981. ISBN 0-13-273426-5.

....iff there exists an asynchronous c morphism from Uf(TS p ) into Uf (TS s ) We now wish to show that the problem of deciding if a pair of finite asynchronous transition systems admits an asynchronous controller finite or otherwise is undecidable. The reduction is from the tiling problem [LP] which is known to be undecidable. In what follows, it will be convenient to talk about the tiling problem as a colouring problem. An instance of the colouring problem is a quadruple CP = C; c in ; R; U ) where C is a finite set of colours, c in 2 C is a distinguished initial colour and R : C ....

H. Lewis and C. H. Papadimitriou: Elements of the theory of computation, Prentice Hall, New Jersey, U.S.A. (1981).

....operations to be executed in parallel on each given molecule. Winfree, et al. [W96, WYS96] proposed an innovative method for LP BMC, that of computation by unmediated self assembly of 2D arrays of DNA molecules, applying known domino tiling techniques (see Buchi [B62] Berger [B66] and [R71, LP81] in combination with recombinant DNA nano fabrication techniques of Seeman et al. [SZC94] The likelihood for successful unmediated self assembly of computations has not been determined (we discuss a simple model of assembly where there may be blockages in self assembly, but more sophisticated ....

....biological applications, for example DNA sequencing, involve large DNA strands. LP BMC methods may allow for the efficient processing for such large DNA and RNA strands. LP BMC via Unmediated Self assembly. Domino tiling techniques were developed by Buchi [B62] Berger [B66] and others [R71, LP81] in the early 1960s, and allow simulation of a 1 tape Turing Machine with S n space (or a 1D parallel array of S processors) running in time T n by construction of an assembly of an S=2 Theta T array of A = ST=2 n 2 =2 tiles. Winfree [W96] also Winfree, et al. [WYS96] proposed to execute ....

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H. R. Lewis and C.H. Papadimitriou Elements of the Theory of Computation, Prentice-Hall, pages 296--300 and 345--348 (1981).

....of the tiling assembly be the number of tiles placed. Berger [B66] also see Buchi [B62] proved that given a finite set of tile types, the tiling problem is undecidable if the extent of tiling is infinite. Direct simulations of a single tape deterministic Turing Machines are given in [R71] and [LP81] pages 296 300) Also, GJP77] see [GJ79] page 257) and [LP81] pages 345 348) proved that the domino tiling problem is NP complete if the extent of tiling is a rectangle of polynomial size. Grunbaum, Branko, and Shepard [GBS87] surveyed these and related results on the complexity of ....

....(also see Buchi [B62] proved that given a finite set of tile types, the tiling problem is undecidable if the extent of tiling is infinite. Direct simulations of a single tape deterministic Turing Machines are given in [R71] and [LP81] pages 296 300) Also, GJP77] see [GJ79] page 257) and [LP81] pages 345 348) proved that the domino tiling problem is NP complete if the extent of tiling is a rectangle of polynomial size. Grunbaum, Branko, and Shepard [GBS87] surveyed these and related results on the complexity of tiling. ffl Computation via Local Assembly. Winfree [W96] proposed a very ....

Lewis, H.R., and C.H. Papadimitriou Elements of the Theory of Computation, Prentice-Hall, pages 296--300 and 345--348 (1981).

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