computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem ...

, a nonelementary problem is a problem that is not a member of the class

ELEMENTARY Elementary may refer to: Arts, entertainment, and media Music * ''Elementary'' (Cindy Morgan album), 2001 * ''Elementary'' (The End album), 2007 * ''Elementary'', a Melvin "Wah-Wah Watson" Ragin album, 1977 Other uses in arts, entertainment, an ...

. As a class it is sometimes denoted as NONELEMENTARY. Examples of nonelementary problems that are nevertheless decidable include: * the problem of regular expression equivalence with complementation * the

decision problem In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding whether a given natura ...

for

monadic second-order logic In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. It is particularly important in the logic of graphs, because of Courcelle's ...

over

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only ...

s (see S2S) * the decision problem for

term algebra Term may refer to: Language *Terminology, context-specific nouns or compound words **Technical term (or ''term of art''), used by specialists in a field ***Scientific terminology, used by scientists *Term (argumentation), part of an argument in d ...

s * satisfiability of

W. V. O. Quine W. may refer to: * SoHo (Australian TV channel) (previously W.), an Australian pay television channel * ''W.'' (film), a 2008 American biographical drama film based on the life of George W. Bush * "W.", the fifth track from Codeine's 1992 EP ''Bar ...

's fluted fragment of

first-order logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over ...

* deciding β-convertibility of two closed terms in

typed lambda calculus A typed lambda calculus is a typed formalism that uses the lambda symbol (\lambda) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a ...

reachability In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s can reach a vertex t (and t is reachable from s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with s a ...

vector addition system A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems. Vector addition systems were introduced by Richard M. Karp and Raymond E. Miller in 1969, and generalized to vector additi ...

s; it is Ackermann-complete. *

Petri nets A Petri net, also known as a place/transition net (PT net), is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite grap ...

; it is Ackermann-complete.

References

Complexity classes {{Comp-sci-theory-stub