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section 6.1
section 6.1

3.6 First-Order Tableau
3.6 First-Order Tableau

Particular Integrals
Particular Integrals

... which is now a standard second-order case. The auxiliary equation is 2k 2 + 2k + 1 = 0 which has complex solutions. Choose a third order polynomial for the particular integral. The general solution turns out to be ...
1 - JustAnswer
1 - JustAnswer

CoursePortfolioCS435
CoursePortfolioCS435

1.1 - ASU
1.1 - ASU

... It’s not clear how to come up with an equation with just one variable in it. However, elimination can be used to come up with two equations which only involve the variables y and z. These equations in turn can be solved for y and z, which in turn will give us the value of x. The bad news is that it ...
Solving Mathematical Puzzles: a Deep Reasoning Challenge
Solving Mathematical Puzzles: a Deep Reasoning Challenge

Comprehensive Guide - Reddingschools.net
Comprehensive Guide - Reddingschools.net

Overview of Artificial Intelligence
Overview of Artificial Intelligence

Chapter 7 - James Bac Dang
Chapter 7 - James Bac Dang

The Effect of Noise on Artificial Intelligence and Meta
The Effect of Noise on Artificial Intelligence and Meta

Document
Document

... Solve each equation. Show all work and check your solution. 1. m + 72 = 100 ...
5.5 SS
5.5 SS

... When we cannot easily relate the bases of an exponential equation, we will use logarithms and their properties to solve them. The methods used to solve exponential equations are outlined below. ...
Lecture 4
Lecture 4

Sparrow2011
Sparrow2011

... For each training set, we performed 24 independent runs of PARAM ILS for 4 (CPU) days each. The parameter configurations found by PARAM ILS for each instance set were all evaluated on subsets of the instances from the SAT 2009 competition to find the best configuration. For the evaluation we have us ...
SHORTCUT IN SOLVING LINEAR EQUATIONS (Basic Step to
SHORTCUT IN SOLVING LINEAR EQUATIONS (Basic Step to

... existing linear equation solving process very different from what they had learned in their countries. Let’s see what the differences are and how can the existing solving process be improved? The basic difference shows itself in the way we teach students on how to solve a linear equation. We teach t ...
Algebra Expressions and Real Numbers
Algebra Expressions and Real Numbers

Linear Equations
Linear Equations

... called simultaneous equations. What is needed here is to find the pair of values (x, y) that satisfies both of these equations. This is what is meant by ‘solving simultaneous equations’. In the example given we can substitute the value for y (4x) from the first equation into the second equation to g ...
1 - Denton ISD
1 - Denton ISD

Inference in First
Inference in First

... • Resolution can be thought of as the bottom-up construction of a search tree, where the leaves are the clauses produced by KB and the negation of the goal • When a pair of clauses generates a new resolvent clause, add a new node to the tree with arcs directed from the resolvent to the two parent cl ...
solve systems of linear equations
solve systems of linear equations

... compare the slopes and intercepts. One solution – the lines will have different slopes. No solution – the lines will have the same slope, but different intercepts. Infinitely many solutions – the lines will have the same slope and the same intercept. ...
File
File

Student Activity: To investigate how to solve f(x) = (x
Student Activity: To investigate how to solve f(x) = (x

pdf - at www.arxiv.org.
pdf - at www.arxiv.org.

Math 308 Solutions Sec. 1.3 Problems(1,3,5,7,8,9,11,12,15,13) page
Math 308 Solutions Sec. 1.3 Problems(1,3,5,7,8,9,11,12,15,13) page

< 1 ... 12 13 14 15 16 17 18 19 20 ... 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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