Jumping Computation: Updating Automata and Grammars for Discontinuous Information Processing

one-head automata, generalized jumping finite automata, one-way jumping finite
automata, multi-head atuomata, double-jumping finite automata, multi-parallel
jumping finite automata, jumping Watson-Creck finite automata, Jumping 5'->3'
Watson-Crick finite automata, sequential jumping grammars, jumping scattered
context grammars, pure jumping grammars, other discontinuous computation devices,
application perspectives, models of DNA computation, debt lemma.

Jumping Computation: Updating Automata and Grammars for Discontinuous Information
Processing is primarily a theoretically oriented treatment of jumping automata
and grammars, covering all essential theoretical topics concerning them,
including their power, properties, and transformations. From a practical
viewpoint, it describes various concepts, methods, algorithms, techniques, case
studies and applications based upon these automata and grammars.

In today's computerized world, the scientific development and study of
computation, referred to as the theory of computation, plays a crucial role. One
important branch, language theory, investigates how to define and study languages
and their models, which formalize algorithms according to which their computation
is executed. These language-defining models are classified into two basic
categories: automata, which define languages by recognizing their words, and
grammars, which generate them. Introduced many decades ago, these rules reflect
classical sequential computation. However, today's computational methods
frequently process information in a  fundamentally different way, frequently
"jumping" over large portions of the information as a whole. This book adapts
classical models to formalize and study this kind of computation properly. Simply
put, during their language-defining process, these adapted versions, called
jumping automata and grammars, jump across the words they work on.

The book selects important models and summarizes key results about them in
a compact and uniform way. It relates each model to a particular form of modern
computation, such as sequential, semiparallel and totally parallel computation.
It explains how the model in question properly reflects and formalizes the
corresponding form of computation, thus allowing us to obtain a systematized body
of mathematically precise knowledge concerning the jumping computation. The book
pays special attention to power, closure properties, and transformations and also
describes many algorithms that modify jumping grammars and automata so they
satisfy some prescribed properties without changing the defined language. The
book will be of great interest to anyone researching the theory of computation
across the fields of computer science, mathematics, engineering, logic and
linguistics.