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Second-Order Functions and Theorems in ACL2

by Alessandro Coglio
"... SOFT (‘Second-Order Functions and Theorems’) is a tool to mimic second-order functions and the-orems in the first-order logic of ACL2. Second-order functions are mimicked by first-order functions that reference explicitly designated uninterpreted functions that mimic function variables. First-order ..."
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SOFT (‘Second-Order Functions and Theorems’) is a tool to mimic second-order functions and the-orems in the first-order logic of ACL2. Second-order functions are mimicked by first-order functions that reference explicitly designated uninterpreted functions that mimic function variables. First-order

Verification of Second-Order Functional Programs

by Vom Fachbereich Informatik, Der Technischen Universität Darmstadt, Diplom-informatiker Markus Axel Aderhold, Aus Darmstadt, Hochschulkennziffer D Abstract
"... Functional programming languages such as Haskell or ML allow the programmer to implement and to use higher-order procedures. A higher-order procedure gets a function as argument and applies this function to some values. For instance, procedure map applies a function to all elements of a list and ret ..."
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. In this thesis we show how the verification of second-order functional programs can be supported by semi-automated theorem provers. Second-order

On the Role of Deception in Second Order Functions

by L. Schoofs, B. Naudts
"... In this paper we study the behavior of genetic algorithms (GAs) on second order functions, more specially on random binary constraint satisfaction problems for which well studied instance generators can be found. We observe that deception does not play an important role in the search for a solution. ..."
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In this paper we study the behavior of genetic algorithms (GAs) on second order functions, more specially on random binary constraint satisfaction problems for which well studied instance generators can be found. We observe that deception does not play an important role in the search for a solution

A Remark On Second Order Functional Differential Systems

by Valter Seda , Stefan Belohorec , 1992
"... It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact R ffi -set and hence nonvoid, compact and connected set in a Fr'echet space. The proof is based on a Kub'acek's ..."
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It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact R ffi -set and hence nonvoid, compact and connected set in a Fr'echet space. The proof is based on a Kub

SGA Search Dynamics on Second Order Functions

by Bart Naudts, Alain Verschoren - Artificial Evolution 97 , 1998
"... . By comparing its search dynamics to that of a simple O(n 2 ) heuristic, we are able to analyze the behavior of the simple genetic algorithm on second order functions, whose optimization is shown to be an NP-equivalent problem. It appears that both algorithms approach these fitness functions in t ..."
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. By comparing its search dynamics to that of a simple O(n 2 ) heuristic, we are able to analyze the behavior of the simple genetic algorithm on second order functions, whose optimization is shown to be an NP-equivalent problem. It appears that both algorithms approach these fitness functions

Boundary value problems for systems of second-order functional differential equations

by Svatoslav Staněk - Proceedings of the 6th Colloquium on the Qualitative Theory of Differential Equations (Szeged , 1999
"... Abstract. Systems of second-order functional differential equations (x ′ (t)+L(x)(t)) ′ = F (x)(t) together with nonlinear functional boundary conditions are considered. Here L: ..."
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Abstract. Systems of second-order functional differential equations (x ′ (t)+L(x)(t)) ′ = F (x)(t) together with nonlinear functional boundary conditions are considered. Here L:

TWO POSITIVE SOLUTIONS FOR SECOND-ORDER FUNCTIONAL AND ORDINARY BOUNDARY-VALUE PROBLEMS

by Kyriakos G. Mavridis, Panagiotis Ch. Tsamatos , 2005
"... In this paper we use a fixed point theorem due to Avery and Henderson to prove, under appropriate conditions, the existence of at least two positive solutions for a second-order functional and ordinary boundaryvalue problem. ..."
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In this paper we use a fixed point theorem due to Avery and Henderson to prove, under appropriate conditions, the existence of at least two positive solutions for a second-order functional and ordinary boundaryvalue problem.

ON MONOTONE SOLUTIONS FOR A NONCONVEX SECOND-ORDER FUNCTIONAL DIFFERENTIAL INCLUSION

by Aurelian Cernea
"... The existence of monotone solutions for a second-order functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φ-convex function of order two. 1 ..."
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The existence of monotone solutions for a second-order functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φ-convex function of order two. 1

ANALYTIC SOLUTION OF CERTAIN SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATION

by Theeradach Kaewong, Piyapong Niamsup , 2006
"... We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x (x[r](z)) = c0z2 + c1(x(z))2 + (c2x[2](z))2 + ·· · + cm(x[m](z))2,m,r ≥ 0. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. ..."
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We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x (x[r](z)) = c0z2 + c1(x(z))2 + (c2x[2](z))2 + ·· · + cm(x[m](z))2,m,r ≥ 0. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1.

Oscillation of second order functional dynamic equations

by Lynn Erbe , Taher Hassan , Allan Peterson - Int. J. Differential Equ. (Submitted
"... Abstract In this paper we investigate the oscillation of a second order nonlinear functional dynamic equation. Our results extend and improve many known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results. ..."
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Abstract In this paper we investigate the oscillation of a second order nonlinear functional dynamic equation. Our results extend and improve many known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.
Results 1 - 10 of 13,010