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Abstract recursion as a foundation for the theory of algorithms

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/malq.19870330107openalex-snapshot

Second‐order and Inductive Definability on Finite Structures

inferredcites →https://doi.org/10.1007/978-1-4612-6228-2openalex-snapshot

The Denotational Description of Programming Languages

inferredcites →https://doi.org/10.1007/978-3-662-11824-5openalex-snapshot

General Recursion Theory

inferredcites →https://doi.org/10.1007/978-94-010-1138-9_12openalex-snapshot

On the Basic Notions in the Theory of Induction

inferredcites →https://doi.org/10.1007/bfb0012779openalex-snapshot

A programming language for the inductive sets, and applications

inferredcites →https://doi.org/10.1007/bfb0012801openalex-snapshot

Domains for denotational semantics

inferredcites →https://doi.org/10.1007/bfb0022533openalex-snapshot

A logical approach to the problem “P=NP?”

inferredcites →https://doi.org/10.1016/0022-0000(80)90032-xopenalex-snapshot

Computable queries for relational data bases

inferredcites →https://doi.org/10.1016/0022-0000(82)90012-5openalex-snapshot

Structure and complexity of relational queries

inferredcites →https://doi.org/10.1016/0096-0551(83)90036-xopenalex-snapshot

Denotational semantics: The scott-strachey approach to programming language theory

inferredcites →https://doi.org/10.1016/0168-0072(85)90036-3openalex-snapshot

Reflection and forcing in E-recursion theory

inferredcites →https://doi.org/10.1016/0168-0072(94)00005-nopenalex-snapshot

Power set recursion

inferredcites →https://doi.org/10.1016/b978-0-7204-2233-7.50022-8openalex-snapshot

FINITE APPROXIMATIONS OF INFINITELY LONG FORMULAS

inferredcites →https://doi.org/10.1016/b978-0-7204-2233-7.50025-3openalex-snapshot

MODEL-THEORETIC INVARIANTS: APPLICATIONS TO RECURSIVE AND HYPERARITHMETIC OPERATIONS

inferredcites →https://doi.org/10.1016/s0049-237x(08)71118-2openalex-snapshot

α-Recursion Theory

inferredcites →https://doi.org/10.1016/s0049-237x(08)71119-4openalex-snapshot

Recursion in Higher Types*

inferredcites →https://doi.org/10.1016/s0049-237x(08)71229-1openalex-snapshot

Axiomatic Recursive Function Theory

inferredcites →https://doi.org/10.1016/s0049-237x(08)71231-xopenalex-snapshot

Axioms for Computation Theories-First Draft

inferredcites →https://doi.org/10.1016/s0049-237x(08)x7092-2openalex-snapshot

Elementary Induction on Abstract Structures

inferredcites →https://doi.org/10.1016/s0049-237x(09)70435-5openalex-snapshot

Inductive Schemata and Recursively Continuous Functionals

inferredcites →https://doi.org/10.1017/9781316717073openalex-snapshot

General Recursion Theory

inferredcites →https://doi.org/10.1017/cbo9780511629181.008openalex-snapshot

Three Aspects of Recursive Enumerability in Higher Types

inferredcites →https://doi.org/10.1049/ip-i-1.1981.0010openalex-snapshot

Introduction to V.L.S.I. Systems

inferredcites →https://doi.org/10.1090/s0002-9947-1959-0102480-9openalex-snapshot

Recursive functionals and quantifiers of finite types. I

inferredcites →https://doi.org/10.1090/s0002-9947-1967-0236010-2openalex-snapshot

Hyperanalytic predicates

inferredcites →https://doi.org/10.1090/s0002-9947-1969-0244045-0openalex-snapshot

Abstract first order computability. I, II

inferredcites →https://doi.org/10.1090/s0002-9947-1969-0249297-9openalex-snapshot

Uniformly reflexive structures: On the nature of gödelizations and relative computability

inferredcites →https://doi.org/10.1090/s0273-0979-1981-14920-xopenalex-snapshot

The theory of recursive functions, approaching its centennial

inferredcites →https://doi.org/10.1093/comjnl/12.1.28openalex-snapshot

Theory of Recursive Functions and Effective Computability

inferredcites →https://doi.org/10.1093/comjnl/6.4.308openalex-snapshot

The Mechanical Evaluation of Expressions

inferredcites →https://doi.org/10.1109/sfcs.1983.5openalex-snapshot

Algebras of feasible functions

inferredcites →https://doi.org/10.1112/blms/4.2.226openalex-snapshot

LOGIC COLLOQUIUM '69

inferredcites →https://doi.org/10.1145/359576.359579openalex-snapshot

Can programming be liberated from the von Neumann style?

inferredcites →https://doi.org/10.1145/367177.367199openalex-snapshot

Recursive functions of symbolic expressions and their computation by machine, Part I

inferredcites →https://doi.org/10.1145/567752.567763openalex-snapshot

Universality of data retrieval languages

inferredcites →https://doi.org/10.1145/800061.808765openalex-snapshot

Languages which capture complexity classes

inferredcites →https://doi.org/10.1145/800070.802187openalex-snapshot

Relational queries computable in polynomial time (Extended Abstract)

inferredcites →https://doi.org/10.1147/rd.126.0465openalex-snapshot

Algebraically Generalized Recursive Function Theory

inferredcites →https://doi.org/10.2307/2269621openalex-snapshot

Metarecursive sets

inferredcites →https://doi.org/10.2307/2271519openalex-snapshot

The next admissible set

inferredcites →https://doi.org/10.2307/2273529openalex-snapshot

Global inductive definability

inferredcites →https://doi.org/10.2307/2316720openalex-snapshot

Theory of Recursive Functions and Effective Computability.

inferredcites →https://doi.org/10.25405/ncl.34123365openalex-snapshot

Formal Specification and Software Development

inferredcites →https://doi.org/10.4064/fm-56-3-325-345openalex-snapshot

Some applications of the notions of forcing and generic sets

inferredcites →https://doi.org/10.5860/choice.47-3209openalex-snapshot

Principles of programming languages

inferredcites →https://doi.org/10.7146/dpb.v11i143.7418openalex-snapshot

A Programming Language for the Inductive Sets, and Applications

inferredcites →https://doi.org/10.7551/mitpress/12274.003.0023openalex-snapshot

Recursive Functions of Symbolic Expressions and Their Computation by Machine (1960)

inferredcites →https://doi.org/10.7907/96kfn-x5548openalex-snapshot

Space-Time Algorithms: Semantics and Methodology

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/malq.19950410110openalex-snapshot

Dimension Versus Number of Variables, and Connectivity, too

inferred← citeshttps://doi.org/10.1006/inco.1998.2746openalex-snapshot

Group Axioms for Iteration

inferred← citeshttps://doi.org/10.1007/3-540-16442-1_12openalex-snapshot

The choice of programming primitives for SETL-like programming languages

inferred← citeshttps://doi.org/10.1007/3-540-45575-2_45openalex-snapshot

Abstract Computability of Non-deterministic Programs over Various Data Structures

inferred← citeshttps://doi.org/10.1007/3-540-50241-6_29openalex-snapshot

Is setl a suitable language for parallel programming — a theoretical approach

inferred← citeshttps://doi.org/10.1007/3-540-51237-3_18openalex-snapshot

A mathematical modeling of pure, recursive algorithms

inferred← citeshttps://doi.org/10.1007/3-540-52885-7_126openalex-snapshot

IMPS : An interactive mathematical proof system

inferred← citeshttps://doi.org/10.1007/978-0-387-68546-5_5openalex-snapshot

Elementary Algorithms and Their Implementations

inferred← citeshttps://doi.org/10.1007/978-3-030-59234-9_6openalex-snapshot

A Survey on Analog Models of Computation

inferred← citeshttps://doi.org/10.1007/978-3-319-22156-4_4openalex-snapshot

Theses for Computation and Recursion on Concrete and Abstract Structures

inferred← citeshttps://doi.org/10.1007/978-3-319-63334-3_2openalex-snapshot

Feferman on Computability

inferred← citeshttps://doi.org/10.1007/978-3-642-27660-6_3openalex-snapshot

What Is an Algorithm?

inferred← citeshttps://doi.org/10.1007/978-94-017-0253-9_7openalex-snapshot

Transitive Closure and the Mechanization of Mathematics

inferred← citeshttps://doi.org/10.1007/bf00881906openalex-snapshot

IMPS: An interactive mathematical proof system

inferred← citeshttps://doi.org/10.1007/bf01069523openalex-snapshot

Composition aspects of programmology. II

inferred← citeshttps://doi.org/10.1007/bf01074922openalex-snapshot

Composition aspects of programmology. I

inferred← citeshttps://doi.org/10.1007/bfb0023759openalex-snapshot

A new approach to abstract data types II computation on ADTs as ordinary computation

inferred← citeshttps://doi.org/10.1016/0168-0072(90)90043-2openalex-snapshot

Parametrization over inductive relations of a bounded number of variables

inferred← citeshttps://doi.org/10.1016/0304-3975(93)90085-8openalex-snapshot

Computational foundations of basic recursive function theory

inferred← citeshttps://doi.org/10.1016/0304-3975(93)90345-topenalex-snapshot

Hereditarily-finite sets, data bases and polynomial-time computability

inferred← citeshttps://doi.org/10.1016/0890-5401(92)90074-popenalex-snapshot

Query languages for hierarchic databases

inferred← citeshttps://doi.org/10.1016/s0049-237x(08)70263-5openalex-snapshot

Some Problems and Results in the Theory of Actually Computable Functions (preliminary abstract)

inferred← citeshttps://doi.org/10.1016/s0049-237x(08)70270-2openalex-snapshot

Finitary inductively presented logics

inferred← citeshttps://doi.org/10.1016/s0049-237x(96)80017-6openalex-snapshot

Bibliography

inferred← citeshttps://doi.org/10.1016/s0049-237x(99)80027-5openalex-snapshot

Recursion on Abstract Structures

inferred← citeshttps://doi.org/10.1016/s0304-3975(96)00248-4openalex-snapshot

The equational logic of fixed points

inferred← citeshttps://doi.org/10.1017/9781108234238openalex-snapshot

Abstract Recursion and Intrinsic Complexity

inferred← citeshttps://doi.org/10.1017/9781108234238.001openalex-snapshot

Introduction

inferred← citeshttps://doi.org/10.1017/9781108234238.002openalex-snapshot

Preliminaries

inferred← citeshttps://doi.org/10.1017/9781108234238.003openalex-snapshot

Recursive (McCarthy) programs

inferred← citeshttps://doi.org/10.1017/9781108234238.004openalex-snapshot

Complexity theory for recursive programs

inferred← citeshttps://doi.org/10.1017/9781108234238.005openalex-snapshot

The homomorphism method

inferred← citeshttps://doi.org/10.1017/9781108234238.006openalex-snapshot

Lower bounds from Presburger primitives

inferred← citeshttps://doi.org/10.1017/9781108234238.007openalex-snapshot

Lower bounds from division with remainder

inferred← citeshttps://doi.org/10.1017/9781108234238.008openalex-snapshot

Lower bounds from division and multiplication

inferred← citeshttps://doi.org/10.1017/9781108234238.009openalex-snapshot

Non-uniform complexity in N

inferred← citeshttps://doi.org/10.1017/9781108234238.010openalex-snapshot

Polynomial nullity (0-testing)

inferred← citeshttps://doi.org/10.1017/9781108234238.011openalex-snapshot

Symbol index

inferred← citeshttps://doi.org/10.1017/9781108234238.012openalex-snapshot

General index

inferred← citeshttps://doi.org/10.1017/9781316718254.015openalex-snapshot

Sense and denotation as algorithm and value

inferred← citeshttps://doi.org/10.1017/9781316755884.004openalex-snapshot

Notions of computability at higher types I

inferred← citeshttps://doi.org/10.1017/9781316755983.010openalex-snapshot

Computability theory: structure or algorithms

inferred← citeshttps://doi.org/10.1017/cbo9780511863196.019openalex-snapshot

Oracles, Infinitary Computation, and the Physics of the Mind

inferred← citeshttps://doi.org/10.1017/cbo9780511863196.020openalex-snapshot

Turing's ‘Oracle’: From Absolute to Relative Computability and Back

inferred← citeshttps://doi.org/10.1017/s0022481200041086openalex-snapshot

The formal language of recursion

inferred← citeshttps://doi.org/10.1017/s0022481200041116openalex-snapshot

Some restrictions on simple fixed points of the integers

inferred← citeshttps://doi.org/10.1017/s0960129500001432openalex-snapshot

A new approach to abstract data types, I Informal development

inferred← citeshttps://doi.org/10.1023/a:1026107209351openalex-snapshot

Guarded Quantification in Least Fixed Point Logic

inferred← citeshttps://doi.org/10.1093/acprof:oso/9780198759591.003.0002openalex-snapshot

Algorithms and the Mathematical Foundations of Computer Science

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.001.0001openalex-snapshot

The Nature of Physical Computation

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.002.0004openalex-snapshot

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0001openalex-snapshot

Introduction

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0002openalex-snapshot

Desiderata of a Theory of Computation

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0003openalex-snapshot

Turing’s Computability

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0004openalex-snapshot

Preamble to Machine Computation

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0005openalex-snapshot

Computation as Step-Satisfaction

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0006openalex-snapshot

Computation as Implementation

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0007openalex-snapshot

Computation as Mechanism

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0008openalex-snapshot

The Semantic View of Computation

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0009openalex-snapshot

An Argument for the Semantic View

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0010openalex-snapshot

Computing as Modeling

inferred← citeshttps://doi.org/10.1093/oso/9780197552384.003.0011openalex-snapshot

Conclusion

inferred← citeshttps://doi.org/10.1109/lics.1991.151633openalex-snapshot

Partial objects in the calculus of constructions

inferred← citeshttps://doi.org/10.14236/ewic/iwfm1999.5openalex-snapshot

A Scheme for Defining Partial Higher-Order Functions by Recursion

inferred← citeshttps://doi.org/10.2307/2275003openalex-snapshot

Annual Meeting of the Association for Symbolic Logic, Los Angeles, 1989

inferred← citeshttps://doi.org/10.3233/fun-2005-67404openalex-snapshot

First and Second Order Recursion on Abstract Data Types

inferred← citeshttps://doi.org/10.7282/t34m9501openalex-snapshot

What algorithms could not be

Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.