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A problem is defined to be PSPACE-complete if it can be solved using a polynomial amount of memory (it belongs to PSPACE) and every problem in PSPACE can be transformed in polynomial time into an equivalent instance of the given problem. [1] The PSPACE-complete problems are widely suspected to be outside the more famous complexity classes P ...
Equivalence problem for star-free regular expressions with squaring. [21] Covering for linear grammars [37] Structural equivalence for linear grammars [38] Equivalence problem for Regular grammars [39] Emptiness problem for ET0L grammars [40] Word problem for ET0L grammars [41] Tree transducer language membership problem for top down finite ...
In order to prove that a given problem in P is P-complete, one typically tries to reduce a known P-complete problem to the given one. In 1999, Jin-Yi Cai and D. Sivakumar, building on work by Ogihara, showed that if there exists a sparse language that is P-complete, then L = P. [1] P-complete problems may be solvable with different time ...
A problem that belongs to NP can be proven to be NP-complete by finding a single polynomial-time many-one reduction to it from a known NP-complete problem. [6] Polynomial-time many-one reductions have been used to define complete problems for other complexity classes, including the PSPACE-complete languages and EXPTIME-complete languages. [7]
The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC. Although a solution to an NP-complete problem can be verified "quickly", there is no known way to find a solution quickly.
Despite the strong empirical evidence and highly visible collapse-inducing disturbances, anticipating collapse is a complex problem. The collapse can happen when the ecosystem's distribution decreases below a minimal sustainable size, or when key biotic processes and features disappear due to environmental degradation or disruption of biotic ...
The term DQC1 has been used to instead refer to decision problems solved by a polynomial time classical circuit that adaptively makes queries to polynomially many DQC1 circuits. [6] In this sense of use, the class naturally contains all of BPP, and the power of the class is focused on the "inherently quantum" power.
A survey of known distNP-complete problems is available online. [6] One area of active research involves finding new distNP-complete problems. However, finding such problems can be complicated due to a result of Gurevich which shows that any distributional problem with a flat distribution cannot be distNP-complete unless EXP = NEXP. [8]