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General Recursion on Second Order Term Algebras
[chapter]

2001
*
Lecture Notes in Computer Science
*

##
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A Completeness Theorem for the Expressive Power of Higher-Order Algebraic Specifications

1997
*
Journal of computer and system sciences (Print)
*

In particular we show that for any countable signature 7 and minimal 7

doi:10.1006/jcss.1997.1489
fatcat:hf55mv6znjcfhkxcw2kjrz2gii
*algebra*A, A has complexity 6 1 1 if, and only if, A has a*recursive**second*-*order*equational specification with constructors and hidden ... We consider the expressive power of a*general*form of higher-*order**algebraic*specification which allows constructors and hidden sorts and operations. ... We acknowledge the helpful comments provided*on*this work by P. Kosiuczenko, B. Mo ller, and M. Wirsing. ...##
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On an Algebraic Foundation of Kinematical Constraints of Pair Operators in a Many-Nucleon System

1976
*
Progress of theoretical physics
*

The

doi:10.1143/ptp.55.1146
fatcat:um7xv6hq3bcjxh4qp5ym5kyrau
*algebraic*foundation of these constraints is given with the use of*algebraic**recursion*formulas. ... Various kinds of kinematical constraints of pair operators play important roles in an*algebraic*approach to the theory of nuclear collective motion. ... Acknowledgements This \vork is performed as a part of the "Annual Research Project for Anharmonic and Non Adiabatic Effects in Nuclear Collective Motion and*Algebraic*Approach" organized by the Research ...##
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Page 1307 of Mathematical Reviews Vol. , Issue 2003B
[page]

2003
*
Mathematical Reviews
*

68N18 Berarducci, Alessandro (I-PISA; Pisa) ; Bohm, Corrado (I-ROME-IS; Rome)

*General**recursion**on**second**order**term**algebras*. ... “In this paper we consider a stronger scheme of*recursion*and 2003b:68091 we prove that it captures all partial*recursive*functions*on**second**order**term**algebras*. ...##
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First- and Second-Order Models of Recursive Arithmetics
[article]

2017
*
arXiv
*
pre-print

We introduce and study first- and

arXiv:1705.05459v1
fatcat:fsiz2psexzdrlpkpxwlxy3co5m
*second*-*order*theories of*recursive*arithmetic ARA_1 and ARA_2 capable of characterizing various computational complexity classes and based*on*function*algebras*A, studied ... The*algebras*determine a*second*-*order*theory in the language L 2 designated by 2 and called the*second*-*order**recursive*arithmetic of ( ). ... Also Thm. 9.10 shuld be*generalized*to all function subalgebras of PRA.*Second*-*Order*Theories for Function*Algebras*. Fix a class of function*algebras*( ). ...##
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Diagonal fixed points in algebraic recursion theory

2005
*
Archive for Mathematical Logic
*

Here we consider this question in the context of

doi:10.1007/s00153-005-0307-x
fatcat:asza4yjrrrfu3logwrxzlru7vi
*algebraic**recursion*theory, whose close connection with combinatory logic recently become apparent. ... calculus) diagonal fixed points in a class of partially*ordered**algebras*which covers both combinatory spaces of Skordev and operative spaces of Ivanov. ... This complexity is undesirable, since these suppositions have to occur as basic axioms, but they were either*second**order*(expressible via*second**order*formulas in the language of the corresponding*algebraic*...##
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On the representation of data in lambda-calculus
[chapter]

1990
*
Lecture Notes in Computer Science
*

At the logical level the data types are defined by

doi:10.1007/3-540-52753-2_47
fatcat:gwodcglcvndcvoy2sszmbuc3me
*second**order*formulas expressing the usual iterative definition of the corresponding*algebras*of*terms*, and the data receive the corresponding iterative ... For simplicity, we state these results for the type of natural numbers, but they hold in fact for all the usual data types defined as multisorted*term**algebras*. ... At the logical level the data types are defined by*second**order*formulas expressing the usual iterative definition of the corresponding*algebras*of*terms*, and the data receive the corresponding iterative ...##
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Solving Algebraic Equations Using Coalgebra

2003
*
RAIRO - Theoretical Informatics and Applications
*

*Algebraic*systems of equations define functions using

*recursion*where parameter passing is permitted. ... rather than just Set; and ii) we define

*algebraic*equations to allow right-hand sides which need not consist of finite

*terms*. ... We

*generalize*

*algebraic*

*terms*to

*recursion*over other

*algebras*such as infinite

*terms*or rational

*terms*using what we call coalgebraic monads. ...

##
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Page 3 of Mathematical Reviews Vol. 29, Issue 1
[page]

1965
*
Mathematical Reviews
*

Liu, Shih-Chao Four types of

*general**recursive*well Notre Dame J. evormal Logic 3 (1962), 15-78,*General**recursive*well-*orderings*of all the natural numbers may, of course, have many non-constructive features ... Let A,, A,, and A,, denote the set of all primitive-,*general*- and partial-*recursive*functions of*one*variable, respectively. ...##
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Page 66 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

The

*second*appendix is a concise description of the first-*order*theory of*ordered*structures. A. A. ... Chapter 1 includes such basic concepts as*generation*, structural induction,*algebraic**recursion*and deduction, equivalence relations, partial*orders*, and terminating relations. ...##
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On the Power of Higher-Order Algebraic Specification Methods

1996
*
Information and Computation
*

These results demonstrate that higher-

doi:10.1006/inco.1996.0007
fatcat:h35bgp6fjbeipcozmtossllkri
*order*initial*algebra*semantics substantially extends the power of both first-*order*initial and first-*order*final*algebra*semantics. ... Soundness and adequacy theorems are presented for the expressive power of higher-*order*initial*algebra*specifications with respect to the arithmetical and analytical hierarchies. ... A*SECOND*-*ORDER*SPECIFICATION OF THE TRUTH DEFINITION OF ARITHMETIC In this section we give a finite*second*-*order*signature 7 PA2 and a*recursive**second*-*order*equational specification E PA2 over 7 PA2 . ...##
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Page 7264 of Mathematical Reviews Vol. , Issue 87m
[page]

1987
*
Mathematical Reviews
*

Associative path

*orderings*are based*on**recursive*path*orderings*(>;po) [N. Dershowitz, Theoret. Comput. Sci. 17 (1982), no. 3, 279-301; MR 83e:68137]. ... A new class of*orderings*for*terms*, associative path*orderings*(>apo), is described. ...##
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Generalization and exact deformations of quantum groups

1997
*
Publications of the Research Institute for Mathematical Sciences
*

The r-matrices obtained here are more

doi:10.2977/prims/1195145535
fatcat:swsmq27o7neg7nfvpzxamv6ho4
*general*in that they are defined*on*the full Kac-Moody*algebras*, the central extensions of the loop groups. ... In other special cases*one*finds new types of coboundary bi-*algebras*. The "standard" universal R-matrix is shown to be the unique solution of a very simple, linear*recursion*relation. ... That Eq. (15.3) implies (15.20) is a simple calculation;*one*collects all*terms*that have exactly*one**generator*in the*second*space. ...##
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A Cost Estimation Technique for Recursive Relational Algebra

2020
*
Proceedings of the 29th ACM International Conference on Information & Knowledge Management
*

In this paper, we propose a new cost estimation technique for

doi:10.1145/3340531.3417460
dblp:conf/cikm/LawalGL20
fatcat:zi23ffpkv5gxfjhyklq4u3e5pq
*recursive**terms*of the extended relational*algebra*. ... Recently, extensions of Codd's classical relational*algebra*to support*recursive**terms*and their optimisation gained renewed interest [10] . ... Results: relative query performance Results: ranking of cost estimations We also run all equivalent*terms*of the plan space P that are*generated*by the optimizer, in*order*to assess how our*term*-picking ...##
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Page 4298 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

94n:03062

*algebra*and semantic universality, and gives a characterization of £-universal*recursively*axiomatizable classes of models in*terms*of the*generalized*Lindenbaum*algebras*of their theories over ... (French summary) [Optimal results*on*the existence of an integer part in*ordered*fields] J. Symbolic Logic 58 (1993), no. 1, 326-333. Let A be an*ordered*field. ...
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