Arto Salomaa

First-Order Programming Theory

Mathematical Background.- 1. Logic and Model Theory.- 2. Inductive Definability.- I Computability.- 3. Introduction to Part I.- 4. Main Properties of Program Schemas.- 5. Extension of Program Schemas.- 6. Program Schemas with Stacks.- 7. Computability.- 8. On Inductive Definability of 1- and 2-Computable Relations.- II Extended Dynamic Logics.- 9. Introduction to Part II.- 10. Description of Program Properties.- 11. Den-based Descriptive Languages.- 12. The Problem of Completeness.- 13. Dynamic Logic Generated by Extension.- 14. Continuous Denotational Semantics.- 15. Definable Denotational Semantics.- III Temporal Characterization of Programs.- 16. Introduction to Part III.- 17. Temporal Logic.- 18. Temporal Logical Description of Program Properties.- 19. Is Temporal Logic Expressible in Dynamic Logic?.- 20. Is Dynamic Logic Expressible in Temporal Logic?.- 21. The Case of Enumerable Models.- 22. Temporal Axiomatization of Program Verification Methods.- IV Programming Logic with Explicit Time.- 23. Introduction to Part IV.- 24. Time Logic.- 25. Definability in Regular Time Theories.- 26. Expressive Power of Time.- Epilogue.- References.- Notations.

Beginnings of Molecular Computing

“We can see only a short distance ahead, but we can see plenty there that needs to be done.” These words of Turing [213] can be taken as an underlying principle of any program for scientific development. Such an underlying principle is very characteristic for research programs in computer science. Advances in computer science are often shown by and remembered from some unexpected demonstration, rather than from a dramatic experiment as in physical sciences. As pointed out by Hartmanis [83], it is the role of such a demo to show the possibility or feasibility of doing what was previously thought to be impossible or not feasible. Often, the ideas and concepts brought about and tested in such demos determine or at least influence the research agenda in computer science. Adleman’s experiment [1] constituted such a demo. This book is about the short distance we can see ahead, and about the theoretical work already done concerning various aspects of molecular computing. The ultimate impact of DNA computing cannot yet be seen; this matter will be further discussed in Sect. 2.4.

DNA: Its Structure and Processing

The term “genetic engineering” is a very broad generic term used to cover all kinds of manipulations of genetic material. For the purpose of this book this term describes the in vitro (hence outside living cell) manipulation of DNA and related molecules. These manipulations may be used to perform various kinds of computations.

Splicing Circular Strings

In certain circumstances — in several bacteria, for instance — the DNA molecules are present in the form of a circular sequence. More generally, we can consider situations where both linear and circular DNA sequences are present. The restriction enzymes can cut both the linear and the circular double stranded sequences, hence recombination by ligation can also appear in such a case. Many variants are possible, because a recombination can have as input two circular strings, or one circular and one linear string, and can have as output one or two circular strings, one or two linear strings, or both a circular and a linear string.

Introduction: DNA Computing in a Nutshell

From silicon to carbon. From microchips to DNA molecules. This is the basic idea in DNA computing. Information-processing capabilities of organic molecules can be used in computers to replace digital switching primitives.

Universality by Finite H Systems

As we have seen in the previous chapter, extended H systems with finite sets of axioms and splicing rules are able to generate only regular languages. As we are looking for generative (computability) models having the power of Turing machines, we have to consider features that can increase the power of H systems. This has been successfully done for Chomsky grammars and other generative mechanisms in the regulated rewriting area and the grammar systems area. Following suggestions from these areas, as well as suggestions offered by the proof of the Basic Universality Lemma (Lemma 7.16), in this chapter we shall consider a series of controlled H systems with finite components which characterize the recursively enumerable languages, hence are computationally complete. From the proofs, we shall also obtain universal computing devices, hence models of “programmable DNA computers based on splicing”.