Salvatore Caporaso - Academia.edu (original) (raw)

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Papers by Salvatore Caporaso

Acta Informatica, Aug 1, 1998

Archive for Mathematical Logic, Dec 1, 1978

arXiv (Cornell University), Sep 23, 2006

arXiv (Cornell University), Dec 8, 2007

Information Processing Letters, 2006

International Journal of Foundations of Computer Science, Sep 1, 1996

We introduce a class of safe Turing machines which execute structured while, if-then- else progra... more We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

Lecture Notes in Computer Science, 2000

A resource-free characterization of some complexity classes is given by means of the predicative ... more A resource-free characterization of some complexity classes is given by means of the predicative recursion and constructive diagonal-ization schemes, and of restrictions to substitution. Among other classes, we predicatively harmonize in the same hierarchy ...

Theoretical Computer Science, 2001

The recursion theorem in the weak form {e}(z) = x(e,z) (universal function not needed) and in Rog... more The recursion theorem in the weak form {e}(z) = x(e,z) (universal function not needed) and in Rogers form ��f(n)(z) = �n(z), and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.

Arxiv preprint arXiv:0712.1279, 2007

Abstract: The recursion theorem in the weak form {e}(z)= x (e, z)(universal function not needed) ... more Abstract: The recursion theorem in the weak form {e}(z)= x (e, z)(universal function not needed) and in Rogers form {n}(z)={{x}(n)}(z) and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.

Journal of Functional Programming, 2001

We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at ... more We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at and above the elementary level) in a transfinite hierarchy of classes of functions [Tscr ]α. Class [Tscr ]α is obtained by means of unlimited operators, namely: a variant Π of the predicative or safe recursion scheme, introduced by Leivant, and by Bellantoni and Cook, if α is a successor; and constructive diagonalization if α is a limit. Substitution (SBST) is discarded because the time complexity classes are not closed under this scheme. [Tscr ]α is a structure for the PR functions finer than [Escr ]α, to the point that we have [Tscr ]ε0 = [Escr ]3 (elementary functions). Although no explicit use is made of hierarchy functions, it is proved that f(n) ∈ [Tscr ]α implies f(n) [les ] nGα(n), where Gα belongs to the slow growing hierarchy (of functions) studied, in particular, by Girard and Wainer.

International Journal of Foundations of Computer Science, 1996

We introduce a class of safe Turing machines which execute structured while, if-then- else progra... more We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

Information Processing Letters, 2006

Proceedings of the 6th WSEAS …, 2007

Archiv für mathematische Logik und Grundlagenforschung, 1980

ABSTRACT

Archiv für Mathematische Logik und Grundlagenforschung, 1978

J. Univers. Comput. Sci., 2000

A class LT 0 of functions computable in a proper sub-class of Lintime is de ned, and formalized i... more A class LT 0 of functions computable in a proper sub-class of Lintime is de ned, and formalized in a system LT0 of monadic and atomic (quanti er-free) logic. In spite of its poor computational complexity power and logical apparatus, this system has enough power to describe its own proof-predicate. Therefore it might qualify as smallest known system in which Godel-like diagonalization can be applied. A proof is given that the identically true functions of LT 0 are productive. Hence this incompleteness phenomenon doesn't depend on the technicalities adopted to show it.

Acta Informatica, Aug 1, 1998

Archive for Mathematical Logic, Dec 1, 1978

arXiv (Cornell University), Sep 23, 2006

arXiv (Cornell University), Dec 8, 2007

Information Processing Letters, 2006

International Journal of Foundations of Computer Science, Sep 1, 1996

We introduce a class of safe Turing machines which execute structured while, if-then- else progra... more We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

Lecture Notes in Computer Science, 2000

A resource-free characterization of some complexity classes is given by means of the predicative ... more A resource-free characterization of some complexity classes is given by means of the predicative recursion and constructive diagonal-ization schemes, and of restrictions to substitution. Among other classes, we predicatively harmonize in the same hierarchy ...

Theoretical Computer Science, 2001

The recursion theorem in the weak form {e}(z) = x(e,z) (universal function not needed) and in Rog... more The recursion theorem in the weak form {e}(z) = x(e,z) (universal function not needed) and in Rogers form ��f(n)(z) = �n(z), and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.

Arxiv preprint arXiv:0712.1279, 2007

Abstract: The recursion theorem in the weak form {e}(z)= x (e, z)(universal function not needed) ... more Abstract: The recursion theorem in the weak form {e}(z)= x (e, z)(universal function not needed) and in Rogers form {n}(z)={{x}(n)}(z) and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.

Journal of Functional Programming, 2001

We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at ... more We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at and above the elementary level) in a transfinite hierarchy of classes of functions [Tscr ]α. Class [Tscr ]α is obtained by means of unlimited operators, namely: a variant Π of the predicative or safe recursion scheme, introduced by Leivant, and by Bellantoni and Cook, if α is a successor; and constructive diagonalization if α is a limit. Substitution (SBST) is discarded because the time complexity classes are not closed under this scheme. [Tscr ]α is a structure for the PR functions finer than [Escr ]α, to the point that we have [Tscr ]ε0 = [Escr ]3 (elementary functions). Although no explicit use is made of hierarchy functions, it is proved that f(n) ∈ [Tscr ]α implies f(n) [les ] nGα(n), where Gα belongs to the slow growing hierarchy (of functions) studied, in particular, by Girard and Wainer.

International Journal of Foundations of Computer Science, 1996

We introduce a class of safe Turing machines which execute structured while, if-then- else progra... more We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

Information Processing Letters, 2006

Proceedings of the 6th WSEAS …, 2007

Archiv für mathematische Logik und Grundlagenforschung, 1980

ABSTRACT

Archiv für Mathematische Logik und Grundlagenforschung, 1978

J. Univers. Comput. Sci., 2000

A class LT 0 of functions computable in a proper sub-class of Lintime is de ned, and formalized i... more A class LT 0 of functions computable in a proper sub-class of Lintime is de ned, and formalized in a system LT0 of monadic and atomic (quanti er-free) logic. In spite of its poor computational complexity power and logical apparatus, this system has enough power to describe its own proof-predicate. Therefore it might qualify as smallest known system in which Godel-like diagonalization can be applied. A proof is given that the identically true functions of LT 0 are productive. Hence this incompleteness phenomenon doesn't depend on the technicalities adopted to show it.