Emergent Computation

Emergent Computation emphasizes the interrelationship of the different classes of languages studied in mathematical linguistics (regular, context-free, context-sensitive, and type 0) with aspects to the biochemistry of DNA, RNA, and proteins. In addition, aspects of sequential machines such as parity checking and semi-groups are extended to the study of the Biochemistry of DNA, RNA, and proteins. Mention is also made of the relationship of algebraic topology, knot theory, complex fields, quaternions, and universal turing machines and the biochemistry of DNA, RNA, and proteins.

Emergent Computation tries to avoid an emphasis upon mathematical abstraction ("elegance") at the expense of ignoring scientific facts known to Biochemists. Emergent Computation is based entirely upon papers published by scientists in well-known and respected professional journals. These papers are based upon current research. A few examples of what is not ignored to gain "elegance":

- DNA exists as triple and quadruple strands

- Watson-Crick complementary bases have mismatches

- There can be more than four bases in DNA

- There are more than sixty-four codons

- There may be more that twenty amino acids in proteins

While Emergent Computation emphasizes bioinformatics applications, the last chapter studies mathematical linguistics applied to areas such as languages found in birds, insects, medical applications, anthropology, etc.

Emergent Computation tries to avoid unnecessary mathematical abstraction while still being rigorous. The demands made upon the knowledge of chemistry or mathematics is minimized as well. The collected technical references are valuable in itself for additional reading.

Emergent Computation is concerned with recent applications of Mathematical Linguistics or Automata Theory. This subject has a primary focus upon "Bioinformatics" (the Genome and arising interest in the Proteome), but the closing chapter also examines applications in Biology, Medicine, Anthropology, etc.

The book is composed of an organized examination of DNA, RNA, and the assembly of amino acids into proteins. Rather than examine these areas from a purely mathematical viewpoint (that excludes much of the biochemical reality), the author uses scientific papers written mostly by biochemists based upon their laboratory observations. Thus while DNA may exist in its double stranded form, triple stranded forms are not excluded. Similarly, while bases exist in Watson-Crick complements, mismatched bases and abasic pairs are not excluded, nor are Hoogsteen bonds. Just as there are four bases naturally found in DNA, the existence of additional bases is not ignored, nor amino acids in addition to the usual complement of 20. Can there be more than "64" possible codons? RNA is examined from the point of view of Nussinov plots.

All information is presented from the point of view of regular, context-free, and context sensitive languages, as well as Turing machines and Sequential Machines (and their corresponding semi-groups). Relationships to other subjects of mathematics such as Complex numbers, Quaternions, Algebraic-Topology, and Knot Theory are also mentioned. An examination is made of Splicing Systems as well as Dominoes. Shortcomings illustrating the dangers of mathematical abstractions that ignore biochemistry are pointed out.

The papers examine the subjects of interest from the point of view of applying language theory to search for new results, but also as biological-automatons (implementations or machines) to do calculations.

This book will be of value to those studying Bioinformatics, Biochemistry, Computer-Science, Mathematical Linguistics, and Biology, as well as Pharmacology (with the possible promise of medically active artificial DNA, RNA, and proteins). Laboratory results to demonstrate the usefulness of the topics discussed are demonstrated both in vitro and in vivo.