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RIGID E-UNIFICATION
RIGID E-UNIFICATION

... solvable by computing these equivalence classes. Shostak proved that for computing the equivalence classes of all terms in ThE s t i , no terms that are not in ThE s t i have to be considered: If s can be derived from t using the equalities in E, then this can be done without using an intermediate t ...
MATH 308 Practice Problems for Examination 1 Fall 2008 1. Is 4x +
MATH 308 Practice Problems for Examination 1 Fall 2008 1. Is 4x +

A few sections on Green`s functions in 1D
A few sections on Green`s functions in 1D

Infinite-Horizon Proactive Dynamic DCOPs
Infinite-Horizon Proactive Dynamic DCOPs

PDF only - at www.arxiv.org.
PDF only - at www.arxiv.org.

Solving Rational Equations 7.5
Solving Rational Equations 7.5

2 - SVHSAlgebra1
2 - SVHSAlgebra1

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Ch 7 Alg 1 07

... Solutions or None at All You can prove that a system has infinitely many solutions or no solution using the same methods to solve the systems as we used before:  Graphing  Substituting  Linear Combinations ...
Classical First-Order Logic Introduction
Classical First-Order Logic Introduction

... Given a term t, a variable x and a formula φ, we say that t is free for x in φ if no free x in φ occurs in the scope of ∀z or ∃z for any variable z occurring in t. From now on we will assume that all substitutions satisfy this condition. That is when performing the φ[t/x] we are always assuming that ...
CS 399: Constructive Logic Final Exam (Sample Solution) Name Instructions
CS 399: Constructive Logic Final Exam (Sample Solution) Name Instructions

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Chapter 1

Powerpoint Lessons for Algebra
Powerpoint Lessons for Algebra

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Scheduling Contract Algorithms on Multiple Processors

... real-valued quality QA (t). QA is called A’s performance profile on the instance. Performance profiles are defined for both interruptible and contract algorithms. If A is interruptible, then QA (t) is the quality of the solution returned by A upon interruption at time t. If A is contract, then QA (t ...
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3. - Cobb Learning

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Answers

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2-4

... for all values of the variable. An equation that is an identity has infinitely many solutions. A contradiction is an equation that is not true for any value of the variable. It has no solutions. ...
Section 7.1 - University of South Florida
Section 7.1 - University of South Florida

... you found in Step 3 back into the expression you found in Step 1. The result is the The solution set is {(−6, −3)}. solution(s). They’re preparing us for multiple ...
DUCT: An Upper Confidence Bound Approach to Distributed
DUCT: An Upper Confidence Bound Approach to Distributed

... for the next feasible solution is started. Infeasible assignments can easily be recognized by the variable that enforces the infeasible constraint. Thirdly, when a node a does not have an infeasible local problem, but all its children reported to be infeasible, a is considered to be infeasible as we ...
PROBLEM SOLVING THROUGH FIRST-ORDER LOGIC
PROBLEM SOLVING THROUGH FIRST-ORDER LOGIC

PDF
PDF

... LP to deal with integrality constraints and are the “bread and butter” of OR. The standard OR approach for solving MIP problems is to use a branch-and-bound search. Branch-and-bound entails solving several LP’s, which are relaxations of the original IP or MIP that provide guidance and tighten bounds ...
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2CH2L11 - VincentPienaar
2CH2L11 - VincentPienaar

2.4 Solving an Equation
2.4 Solving an Equation

Solving Addition and Subtraction Equations
Solving Addition and Subtraction Equations

... The Giants scored 13 points in a game against Dallas. They scored 7 points for a touchdown and the rest of their points for field goals. How many points did they score on field goals? Let f represent the field goal points. ...
< 1 ... 6 7 8 9 10 11 12 13 14 ... 33 >

Unification (computer science)

Unification, in computer science and logic, is an algorithmic process of solving equations between symbolic expressions.Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactical unification, otherwise semantical, or equational unification, or E-unification, or unification modulo theory.A solution of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a complete, and minimal substitution set, that is, a set covering all its solutions, and containing no redundant members. Depending on the framework, a complete and minimal substitution set may have at most one, at most finitely many, or possibly infinitely many members, or may not exist at all. In some frameworks it is generally impossible to decide whether any solution exists. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.For example, using x,y,z as variables, the singleton equation set { cons(x,cons(x,nil)) = cons(2,y) } is a syntactic first-order unification problem that has the substitution { x ↦ 2, y ↦ cons(2,nil) } as its only solution.The syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms; however, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite trees.The semantic first-order unification problem { a⋅x = x⋅a } has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative; the same problem, viewed in an abelian group, where (⋅) is considered also commutative, has any substitution at all as a solution.The singleton set { a = y(x) } is a syntactic second-order unification problem, since y is a function variable.One solution is { x ↦ a, y ↦ (identity function) }; another one is { y ↦ (constant function mapping each value to a), x ↦ (any value) }.The first formal investigation of unification can be attributed to John Alan Robinson, who used first-order syntactical unification as a basic building block of his resolution procedure for first-order logic, a great step forward in automated reasoning technology, as it eliminated one source of combinatorial explosion: searching for instantiation of terms. Today, automated reasoning is still the main application area of unification.Syntactical first-order unification is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms.Semantic unification is used in SMT solvers and term rewriting algorithms.Higher-order unification is used in proof assistants, for example Isabelle and Twelf, and restricted forms of higher-order unification (higher-order pattern unification) are used in some programming language implementations, such as lambdaProlog, as higher-order patterns are expressive, yet their associated unification procedure retains theoretical properties closer to first-order unification.
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