Subset-Equational Language - definition. What is Subset-Equational Language
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%ما هو (من)٪ 1 - تعريف

DECISION PROBLEM IN COMPUTER SCIENCE
Subset sum; Subset-sum problem; Subset sums; Subset Sum; Sum of subsets; Subset-sum

Subset-Equational Language      
(SEL) A declarative language for set processing by Bharat Jayaraman with subset and equational program clauses; {pattern matching} over sets (it supports efficient iteration over sets); annotations to say which functions distribute over union in which arguments (for point-wise/incremental computation over sets); defining transitive closures through circular constraints (implemented by mixed top-down/memoisation and bottom-up strategy); meta-programming and simple higher-order programming; modest user-interface including tracing. The SEL compiler, written in Quintus Prolog, generates WAM-like code, extended to deal with set-matching, memoisation, and the novel control structure of the language. The run-time system is written in C. ftp://ftp.cs.buffalo.edu/users/bharat/SEL2. E-mail: Bharat Jayaraman <bharat@cs.buffalo.edu>. ["Towards a Broader Basis for Logic Programming", B. Jayaraman, TR CS Dept, SUNY Buffalo, 1990]. ["Set Abstraction in Functional and Logic Programming", F.S.K. Silbermann <fs@cs.tulane.edu> et al, ACM Proc 1989]. (1994-12-15)
Cofinal (mathematics)         
IN ORDER THEORY, A SUBSET 𝑌 OF A POSET 𝑋 SUCH THAT FOR ANY ELEMENT OF 𝑋, THERE EXISTS AN ELEMENT OF 𝑌 LARGER THAN IT
Cofinal subset; Cofinal function; Cofinal sequence; Cofinal net; Coinitial; Cofinal set; Final function
In mathematics, a subset B \subseteq A of a preordered set (A, \leq) is said to be cofinal or frequent in A if for every a \in A, it is possible to find an element b in B that is "larger than a" (explicitly, "larger than a" means a \leq b).
Coinitial         
IN ORDER THEORY, A SUBSET 𝑌 OF A POSET 𝑋 SUCH THAT FOR ANY ELEMENT OF 𝑋, THERE EXISTS AN ELEMENT OF 𝑌 LARGER THAN IT
Cofinal subset; Cofinal function; Cofinal sequence; Cofinal net; Coinitial; Cofinal set; Final function
·adj Having a common beginning.

ويكيبيديا

Subset sum problem

The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . The problem is known to be NP-hard. Moreover, some restricted variants of it are NP-complete too, for example:

  • The variant in which all inputs are positive.
  • The variant in which inputs may be positive or negative, and T = 0 {\displaystyle T=0} . For example, given the set { 7 , 3 , 2 , 9000 , 5 , 8 } {\displaystyle \{-7,-3,-2,9000,5,8\}} , the answer is yes because the subset { 3 , 2 , 5 } {\displaystyle \{-3,-2,5\}} sums to zero.
  • The variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i.e., T = 1 2 ( a 1 + + a n ) {\displaystyle T={\frac {1}{2}}(a_{1}+\dots +a_{n})} . This special case of SSP is known as the partition problem.

SSP can also be regarded as an optimization problem: find a subset whose sum is at most T, and subject to that, as close as possible to T. It is NP-hard, but there are several algorithms that can solve it reasonably quickly in practice.

SSP is a special case of the knapsack problem and of the multiple subset sum problem.