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Lecture Notes in Computer Science
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
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
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. ...
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
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
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
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
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. ...
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. ...
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
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. ...
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
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  . ... 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
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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