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Book Categories |
Preface | ||
I | Logics of Algorithmic Properties | 1 |
Algorithmic properties of structures | 3 | |
Constructible maps | 21 | |
Remarks on the theory of geometrical constructions | 31 | |
Proof theory and the accuracy of computations | 45 | |
Algorithmic approximations | 53 | |
Structure and meaning of elementary programs | 73 | |
An algorithmic model of strict finitism | 87 | |
The logic of "can do" | 97 | |
II | Galois Theory and the Structure of Problems | 107 |
On the solvability of algorithmic problems | 109 | |
Towards a Galois theory of algorithmic problems | 131 | |
Structural relations between programs and problems | 137 | |
Lower bounds by Galois theory | 151 | |
Generalized Galois theory and its application to complexity | 157 | |
III | An Algebraization of Algorithmics | 183 |
Algebras and combinators | 185 | |
Representations of varieties in combinatory algebras | 189 | |
Equations in combinatory algebras | 199 | |
Cumulative logic programs and modeling | 205 | |
Formal models of computation in which data are processes: theory and applications | 217 | |
Sketch of a new discipline of modeling | 231 | |
Combinatory differential fields | 243 |
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