Word problem for groups
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two wor
Mortality (computability theory)
In computability theory, the mortality problem is a decision problem which can be stated as follows: Given a Turing machine, decide whether it halts when run on any configuration (not necessarily a st
Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a corre
List of undecidable problems
In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct
Scott–Curry theorem
In mathematical logic, the Scott–Curry theorem is a result in lambda calculus stating that if two non-empty sets of lambda terms A and B are closed under beta-convertibility then they are recursively
Rice's theorem
In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the program's behavior (for instance, does the pro
Entscheidungsproblem
In mathematics and computer science, the Entscheidungsproblem (pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm], German for 'decision problem') is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. T
RE (complexity)
In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amou
Emptiness problem
In theoretical computer science and formal language theory, a formal language is empty if its set of valid sentences is the empty set. The emptiness problem is the question of determining whether a la
Trakhtenbrot's theorem
In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order logic on the class of all finite models i
Adian–Rabin theorem
In the mathematical subject of group theory, the Adian–Rabin theorem is a result that states that most "reasonable" properties of finitely presentable groups are algorithmically undecidable. The theor
Halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to ru
Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any g
Post correspondence problem
The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the Entscheidungsproblem it is often use
Wang tile
Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on ea
Spectral gap (physics)
In quantum mechanics, the spectral gap of a system is the energy difference between its ground state and its first excited state. The mass gap is the spectral gap between the vacuum and the lightest p
Group isomorphism problem
In abstract algebra, the group isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem was formulate