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General Recursion on Second Order Term Algebras [chapter]

Alessandro Berarducci, Corrado Böhm
2001 Lecture Notes in Computer Science  
doi:10.1007/3-540-45127-7_4 fatcat:err4w6pcg5bipimbehtg4wbp2u

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

Karl Meinke
1997 Journal of computer and system sciences (Print)  
In particular we show that for any countable signature 7 and minimal 7 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.  ... 
doi:10.1006/jcss.1997.1489 fatcat:hf55mv6znjcfhkxcw2kjrz2gii

On an Algebraic Foundation of Kinematical Constraints of Pair Operators in a Many-Nucleon System

S. Nishiyama
1976 Progress of theoretical physics  
The 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  ... 
doi:10.1143/ptp.55.1146 fatcat:um7xv6hq3bcjxh4qp5ym5kyrau

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.  ... 

First- and Second-Order Models of Recursive Arithmetics [article]

Ján Kľuka, Paul J. Voda
2017 arXiv   pre-print
We introduce and study first- and 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 ( ).  ... 
arXiv:1705.05459v1 fatcat:fsiz2psexzdrlpkpxwlxy3co5m

Diagonal fixed points in algebraic recursion theory

Jordan Zashev
2005 Archive for Mathematical Logic  
Here we consider this question in the context of 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  ... 
doi:10.1007/s00153-005-0307-x fatcat:asza4yjrrrfu3logwrxzlru7vi

On the representation of data in lambda-calculus [chapter]

Michel Parigot
1990 Lecture Notes in Computer Science  
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  ...  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  ... 
doi:10.1007/3-540-52753-2_47 fatcat:gwodcglcvndcvoy2sszmbuc3me

Solving Algebraic Equations Using Coalgebra

Federico De Marchi, Neil Ghani, Christoph Lüth
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.  ... 
doi:10.1051/ita:2003021 fatcat:ksands7b4jfibpswdf2pomytg4

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.  ... 

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.  ... 

On the Power of Higher-Order Algebraic Specification Methods

P. Kosiuczenko, K. Meinke
1996 Information and Computation  
These results demonstrate that higher-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 .  ... 
doi:10.1006/inco.1996.0007 fatcat:h35bgp6fjbeipcozmtossllkri

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.  ... 

Generalization and exact deformations of quantum groups

Christian Frønsdal
1997 Publications of the Research Institute for Mathematical Sciences  
The r-matrices obtained here are more 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.  ... 
doi:10.2977/prims/1195145535 fatcat:swsmq27o7neg7nfvpzxamv6ho4

A Cost Estimation Technique for Recursive Relational Algebra

Muideen Lawal, Pierre Genevès, Nabil Layaïda
2020 Proceedings of the 29th ACM International Conference on Information & Knowledge Management  
In this paper, we propose a new cost estimation technique for 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  ... 
doi:10.1145/3340531.3417460 dblp:conf/cikm/LawalGL20 fatcat:zi23ffpkv5gxfjhyklq4u3e5pq

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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