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Complexity: A Language-Theoretic Point of View

  • Cristian Calude
  • Juraj Hromkovič
Chapter

Abstract

The theory of computation and complexity theory are fundamental parts of current theoretical computer science. They study the borders between possible and impossible in information processing, quantitative rules governing discrete computations (how much work (computational resources) has to be done (have to be used) and suffices (suffice) to algorithmically solve various computing problems), algorithmical aspects of complexity, optimization, approximation, reducibility, simulation, communication, knowledge representation, information, etc. Historically, theoretical computer science started in the 1930s with the theory of computation (computability theory) giving the exact formal border between algorithmically solvable computing problems and problems which cannot be solved by any program (algorithm). The birth of complexity theory can be set in the 1960s when computers started to be widely used and the inner difficulty of computing problems started to be investigated. At that time people defined quantitative complexity measures enabling one to compare the efficiency of computer programs and to study the computational hardness of computing problems as an inherent property of problems. The abstract part of complexity theory has tried to classify computing problems according to their hardness (computational complexity) while the algorithmic part of complexity theory has dealt with the development of methods for the design of effective algorithms for concrete problems.

Keywords

Turing Machine Regular Language Finite Automaton Universal Grammar Input Tape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Cristian Calude
  • Juraj Hromkovič

There are no affiliations available

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