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60
A New RecursionTheoretic Characterization Of The Polytime Functions
 COMPUTATIONAL COMPLEXITY
, 1992
"... We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham. ..."
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Cited by 179 (7 self)
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We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham.
The Complexity Of Propositional Proofs
 Bulletin of Symbolic Logic
, 1995
"... This paper of Tseitin is a landmark as the first to give nontrivial lower bounds for propositional proofs; although it predates the first papers on ..."
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Cited by 103 (2 self)
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This paper of Tseitin is a landmark as the first to give nontrivial lower bounds for propositional proofs; although it predates the first papers on
The History and Status of the P versus NP Question
, 1992
"... this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the re ..."
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Cited by 50 (0 self)
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this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the realization that certain problems are algorithmically unsolvable. At around this time, forerunners of the programmable computing machine were beginning to appear. As mathematicians contemplated the practical capabilities and limitations of such devices, computational complexity theory emerged from the theory of algorithmic unsolvability. Early on, a particular type of computational task became evident, where one is seeking an object which lies
Predicative Recursion and Computational Complexity
, 1992
"... The purpose of this thesis is to give a "foundational" characterization of some common complexity classes. Such a characterization is distinguished by the fact that no explicit resource bounds are used. For example, we characterize the polynomial time computable functions without making any direct r ..."
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Cited by 45 (3 self)
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The purpose of this thesis is to give a "foundational" characterization of some common complexity classes. Such a characterization is distinguished by the fact that no explicit resource bounds are used. For example, we characterize the polynomial time computable functions without making any direct reference to polynomials, time, or even computation. Complexity classes characterized in this way include polynomial time, the functional polytime hierarchy, the logspace decidable problems, and NC. After developing these "resource free" definitions, we apply them to redeveloping the feasible logical system of Cook and Urquhart, and show how this firstorder system relates to the secondorder system of Leivant. The connection is an interesting one since the systems were defined independently and have what appear to be very different rules for the principle of induction. Furthermore it is interesting to see, albeit in a very specific context, how to retract a second order statement, ("inducti...
Theories for Complexity Classes and their Propositional Translations
 Complexity of computations and proofs
, 2004
"... We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus. ..."
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Cited by 30 (7 self)
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We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus.
Characterizations of the Basic Feasible Functionals of Finite Type (Extended Abstract)
 Feasible Mathematics: A Mathematical Sciences Institute Workshop
, 1990
"... Stephen A. Cook and Bruce M. Kapron Department of Computer Science University of Toronto Toronto, Canada M5S 1A4 1 Introduction Functionals are functions which take natural numbers and other functionals as arguments and return natural numbers as values. The class of "feasible" functionals of finit ..."
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Cited by 27 (6 self)
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Stephen A. Cook and Bruce M. Kapron Department of Computer Science University of Toronto Toronto, Canada M5S 1A4 1 Introduction Functionals are functions which take natural numbers and other functionals as arguments and return natural numbers as values. The class of "feasible" functionals of finite type was introduced in [6] via the typed lambda calculus, and used to interpret certain formal systems of arithmetic: systems capturing the notion of "feasibly constructive proof" (we equate feasibility with polynomial time computability) . Here we name the functionals of [6] the basic feasible functionals and justify the designation by presenting results which include two programming style characterizations of the class. We also give examples of both feasible and infeasible functionals, and argue that the notion plays a natural role in complexity theory. Type 2 functionals take numbers and ordinary numerical functions as arguments. When these argument functions are 01 valued (i.e. sets) ...
A New Method for Establishing Conservativity of Classical Systems Over Their Intuitionistic Version
"... this paper we present such a method. Applied to I \Sigma ..."
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Cited by 16 (1 self)
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this paper we present such a method. Applied to I \Sigma
Theories With SelfApplication and Computational Complexity
 Information and Computation
, 2002
"... Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but not ne ..."
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Cited by 12 (9 self)
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Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but not necessarily total. It has turned out that theories with selfapplication provide a natural setting for studying notions of abstract computability, especially from a prooftheoretic perspective.