Mutation systems

We propose mutation systems as a model of the evolution of a string subject to the effects of mutations and a fitness function. One fundamental question about such a system is whether knowing the rules for mutations and fitness, we can predict whether it is possible for one string to evolve into another. To explore this issue we define a specific kind of mutation system with point mutations and a fitness function based on conserved strongly k-testable string patterns. We show that for any k greater than 1, such systems can simulate computation by both finite state machines and asynchronous cellular automata. The cellular automaton simulation shows that in this framework, universal computation is possible and the question of whether one string can evolve into another is undecidable. We also analyze the efficiency of the finite state machine simulation assuming random point mutations.

[1]  R. Adams.  Proceedings , 1947 .

[2]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[3]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[4]  William Stafford Noble,et al.  Assessing computational tools for the discovery of transcription factor binding sites , 2005, Nature Biotechnology.

[5]  Colin R. Reeves,et al.  Evolutionary computation: a unified approach , 2007, Genetic Programming and Evolvable Machines.

[6]  Martin Tompa,et al.  Discovery of regulatory elements in vertebrates through comparative genomics , 2005, Nature Biotechnology.

[7]  Janusz A. Brzozowski,et al.  Characterizations of locally testable events , 1973, Discret. Math..

[8]  Partha S. Vasisht.  Computational Analysis of Microarray Data , 2003 .

[9]  Enrique Vidal,et al.  Inference of k-Testable Languages in the Strict Sense and Application to Syntactic Pattern Recognition , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Peter Leupold,et al.  Computing by observing: Simple systems and simple observers , 2011, Theor. Comput. Sci..

[11]  Robert McNaughton,et al.  Algebraic decision procedures for local testability , 1974, Mathematical systems theory.

[12]  Satoshi Kobayashi,et al.  Learning Local Languages and Their Application to DNA Sequence Analysis , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Satoshi Kobayashi,et al.  Learning Concatenations of Locally Testable Languages from Positive Data , 1994, AII/ALT.

[14]  James Aspnes,et al.  Mutation systems , 2013, Int. J. Comput. Math..

[15]  Peter Leupold,et al.  Evolution and observation--a non-standard way to generate formal languages , 2004, Theor. Comput. Sci..

[16]  A. Sandelin,et al.  Applied bioinformatics for the identification of regulatory elements , 2004, Nature Reviews Genetics.

[17]  Jarkko Kari,et al.  Theory of cellular automata: A survey , 2005, Theor. Comput. Sci..

[18]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[19]  Mats G. Nordahl,et al.  Universal Computation in Simple One-Dimensional Cellular Automata , 1990, Complex Syst..

[20]  B. Alberts,et al.  Molecular Biology of the Cell (Fifth Edition) , 2008 .

[21]  Sam M. Kim,et al.  A Polynomial Time Algorithm for the Local Testability Problem of Deterministic Finite Automata , 1989, WADS.

[22]  Leslie G. Valiant,et al.  Evolvability , 2009, JACM.

[23]  Tom Head,et al.  Splicing Representations of Strictly Locally Testable Languages , 1998, Discret. Appl. Math..