computability
Can machines solve?
Computability concerns whether a problem can be solved by an algorithm—a finite set of mechanical steps that produces an answer.
In computer science and mathematical logic, a function is computable if a theoretical machine could calculate it given unlimited time and memory.
Some problems are provably uncomputable: no algorithm can ever solve them.
The halting problem demonstrated the limits of computability.
Lacking possible proof
- decidableAlgorithmically resolvable
- recursiveDefined in terms of itself
- solvableCapable of resolution
- unsolvableImpossible to resolve
Church-Turing thesis · termination · reducibility · oracle · enumeration · recognizable
Mathematical model of computation
- tapeAdhesive strip on roll
- head movementRepositioning of the skull
- acceptanceConsent to receive
- configurationArrangement of parts
Impossible to manage
- tractableEasily managed or controlled
- feasibleCapable of being done
- infeasibleNot capable of achievement
- reducibilityCapacity for simplification
hardness · worst-case · asymptotic · lower bound · upper bound
Accepted starting principles
- proofsDemonstrations of truth
- consistencyReliable adherence to standards
- completenessState of being whole
- formalismPrivileging structure over substance
soundness · arithmetic · second-order · definability · expressibility · provability
Involving repeated cycles
- mechanizableAble to be automated
- step-by-stepIn sequential stages
- well-definedHaving clear boundaries
- specificationDetailed technical requirement
undecidable
Lacking possible proof
unsolvable · Church-Turing thesis · termination · reducibility · oracle · enumeration · recognizable
Turing machine
Mathematical model of computation
- tapeAdhesive strip on roll
- head movementRepositioning of the skull
- acceptanceConsent to receive
intractable
Impossible to manage
- tractableEasily managed or controlled
- feasibleCapable of being done
- infeasibleNot capable of achievement
reducibility · hardness · worst-case · asymptotic · lower bound · upper bound
axioms
Accepted starting principles
- proofsDemonstrations of truth
- consistencyReliable adherence to standards
- completenessState of being whole
formalism · soundness · arithmetic · second-order · definability · expressibility · provability
iterative
Involving repeated cycles
- mechanizableAble to be automated
- step-by-stepIn sequential stages
- well-definedHaving clear boundaries
computer, compute, computing, computers, computed, computation, computes, computable, computations