6+7 definitions Flashcards
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
3SAT
The decision problem of whether there is an interpretation that makes a 3CNF propositional logic formula true.
Karp reduction
A polynomial-time reduction
kCNF
a formula is in kCNF if each conjunct contains at most k literals.
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
SAT
The decision problem of whether there is an interpretation that makes a propositional logic formula true
NP complete
A problem that is in NP and is NP Hard
NP Hard
A problem that is at least as hard as any problem in NP
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.
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.
Intractable
A computable problem that does not have a polynomial-time solution
lower bound
a proof that shows problem X requires at least x complexity
upper bound
An algorithm that shows X requires at most x complexity
P
The class of tractable problems - problems with polynomial-time solutions
Tractable
Problems that can be solved by algorithms in polynomial time.
Equivalence Problem
The problem of deciding whether two programs produce the exact same outputs for the same inputs. Th equivalence problem is non computable
Totality Problem
The problem of deciding whether a program halts for all inputs. The totality problem is non computable
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.
DPNuc the uncomputable decision problem
returns 1 for an input i and if DPNuc(i) does not return 1, else 0
Turing complete
If an algo can be used to simulate any other algo
Halting problem
whether an algorithm halts for a given input. This is uncomputable and NP Hard
Church-Turing thesis
Any algo can be represented by a Turing machine
