3,132 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A Computable Economist’s Perspective on Computational Complexity
A computable economist.s view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, non-deterministic computations, completeness, reducibility and verifiability - all three of the latter concepts had their origins on what may be called "Post's Program of Research for Higher Recursion Theory". Approximations, computations and constructions are also emphasised. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix.
A Computable Economist’s Perspective on Computational Complexity
A computable economist's view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, non-deterministic computations, completeness, reducibility and verifiability - all three of the latter concepts had their origins on what may be called 'Post's Program of Research for Higher Recursion Theory'. Approximations, computations and constructions are also emphasised. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus
In the paper we define three new complexity classes for Turing Machine
undecidable problems inspired by the famous Cook/Levin's NP-complete complexity
class for intractable problems. These are U-complete (Universal complete),
D-complete (Diagonalization complete) and H-complete (Hypercomputation
complete) classes. We started the population process of these new classes. We
justify that some super-Turing models of computation, i.e., models going beyond
Turing machines, are tremendously expressive and they allow to accept arbitrary
languages over a given alphabet including those undecidable ones. We prove also
that one of such super-Turing models of computation -- the \$-Calculus,
designed as a tool for automatic problem solving and automatic programming, has
also such tremendous expressiveness. We investigate also completeness of cost
metrics and meta-search algorithms in \$-calculus
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