Flashcards in 6+7 definitions Deck (22)

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## PSPACE

### A problem belonds to PSPACE if and only if the amount of memory it takes to solve it grows polynomially with the input size

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## 3SAT

### The decision problem of whether there is an interpretation that makes a 3CNF propositional logic formula true.

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## Karp reduction

### A polynomial-time reduction

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## kCNF

### a formula is in kCNF if each conjunct contains at most k literals.

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## CNF

### A formula in CNF consists of a conjunction of disjunctions apart from that which contains only one conjunct or that with one of more disjunctions with a single disjunct

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## SAT

### The decision problem of whether there is an interpretation that makes a propositional logic formula true

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## NP complete

### A problem that is in NP and is NP Hard

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## NP Hard

### A problem that is at least as hard as any problem in NP

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## NP

### A decision problem is in NP if for the inputs where the answer is 1, there exists a certificate that can be checked in polynomial time.

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## TSP

### Given a weighted complete graph, decide whether there is a cycle that passes through every node exactly once except for the start and end node as they are the same, an whose total weight is at most k. The TSP is always relative to a value for k.

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## Intractable

### A computable problem that does not have a polynomial-time solution

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## lower bound

### a proof that shows problem X requires at least x complexity

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## upper bound

### An algorithm that shows X requires at most x complexity

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## P

### The class of tractable problems - problems with polynomial-time solutions

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## Tractable

### Problems that can be solved by algorithms in polynomial time.

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## Equivalence Problem

### The problem of deciding whether two programs produce the exact same outputs for the same inputs. Th equivalence problem is non computable

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## Totality Problem

### The problem of deciding whether a program halts for all inputs. The totality problem is non computable

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## Reduction

### A reduction of one problem A to another problem B is a demonstration that a solution for problem B can be used to solve the original problem A. The demonstration involves an algo that transforms inputs of problem A into inputs of problem B, such that the outputs for problem B correspond with the outputs for problem A.

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## DPNuc the uncomputable decision problem

### returns 1 for an input i and if DPNuc(i) does not return 1, else 0

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## Turing complete

### If an algo can be used to simulate any other algo

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## Halting problem

### whether an algorithm halts for a given input. This is uncomputable and NP Hard

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