Light-based string matching

String matching is a very important problem in computer science. The problem consists in finding all the occurrences of a pattern P of length m in a text T of length n. We describe a special device which can do string matching by performing n−m + 1 text-to-pattern comparisons. The proposed device uses light and optical filters for performing computations. Two physical implementations are proposed. One of them uses colored glass and the other one uses polarizing filters. The strengths and the weaknesses of each method are deeply discussed.

[1]  M. Paniccia,et al.  A continuous-wave Raman silicon laser , 2005, Nature.

[2]  Livio Colussi Correctness and Efficiency of the Pattern Matching Algorithms , 1991, Inf. Comput..

[3]  M. Panicia,et al.  The silicon solution [silicon photonics] , 2005, IEEE Spectrum.

[4]  Dominik Schultes Rainbow Sort: Sorting at the Speed of Light , 2004, Natural Computing.

[5]  Richard Cole,et al.  Tighter Upper Bounds on the Exact Complexity of String Matching , 1997, SIAM J. Comput..

[6]  Thomas J. Naughton,et al.  Model of computation for Fourier optical processors , 2000, International Topical Meeting on Optics in Computing.

[7]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[8]  Dror G. Feitelson Optical computing - a survey for computer scientists , 1988 .

[9]  Richard Cole,et al.  Tighter Lower Bounds on the Exact Complexity of String Matching , 1995, SIAM J. Comput..

[10]  Leonidas J. Guibas,et al.  A New Proof of the Linearity of the Boyer-Moore String Searching Algorithm , 1980, SIAM J. Comput..

[11]  W. Welford Principles of optics (5th Edition): M. Born, E. Wolf Pergamon Press, Oxford, 1975, pp xxviii + 808, £9.50 , 1975 .

[12]  Raffaele Giancarlo,et al.  On the Exact Complexity of String Matching: Upper Bounds , 1992, SIAM J. Comput..

[13]  Raffaele Giancarlo,et al.  The Boyer-Moore-Galil String Searching Strategies Revisited , 1986, SIAM J. Comput..

[14]  G. Agrawal Fiber‐Optic Communication Systems , 2021 .

[15]  J H Reif,et al.  Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive. , 1997, Applied optics.

[16]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[17]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[18]  Joseph W. Goodman,et al.  Architectural development of optical data processing systems , 1982 .

[19]  Raffaele Giancarlo,et al.  On the Exact Complexity of String Matching: Lower Bounds , 1991, SIAM J. Comput..

[20]  Thomas J. Naughton,et al.  An optical model of computation , 2005, Theor. Comput. Sci..

[21]  Robert S. Boyer,et al.  A fast string searching algorithm , 1977, CACM.

[22]  Jerome Faist Optoelectronics: Silicon shines on , 2005, Nature.

[23]  Alexander Fang,et al.  An all-silicon Raman laser , 2005, Nature.

[24]  Thomas J. Naughton,et al.  Implementations of a Model of Physical Sorting , 2008, Int. J. Unconv. Comput..

[25]  Donald E. Knuth,et al.  Fast Pattern Matching in Strings , 1977, SIAM J. Comput..

[26]  Wojciech Plandowski,et al.  Speeding Up Two String-Matching Algorithms , 1992, STACS.

[27]  Mihai Oltean A Light-Based Device for Solving the Hamiltonian Path Problem , 2006, UC.

[28]  Jay N. Damask,et al.  Polarization Optics in Telecommunications , 2004 .

[29]  Leonidas J. Guibas,et al.  A new proof of the linearity of the Boyer-Moore string searching algorithm , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[30]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .