In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE, the class of decision problems solvable in polynomial space, because a solution to any one such problem could easily be used to solve any other problem in PSPACE.
Problems known to be PSPACE-complete include determining properties of regular expressions and context-sensitive grammars, determining the truth of quantified Boolean formulas, step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games.
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.
The PSPACE-complete problems are widely suspected to be outside the more famous complexity classes P (polynomial time) and NP (non-deterministic polynomial time), but that is not known. It is known that they lie outside of the class NC, a class of problems with highly efficient parallel algorithms, because problems in NC can be solved in an amount of space polynomial in the logarithm of the input size, and the class of problems solvable in such a small amount of space is strictly contained in PSPACE by the space hierarchy theorem.
The transformations that are usually considered in defining PSPACE-completeness are polynomial-time many-one reductions, transformations that take a single instance of a problem of one type into an equivalent single instance of a problem of a different type. However, it is also possible to define completeness using Turing reductions, in which one problem can be solved in a polynomial number of calls to a subroutine for the other problem.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position), Game tree size (total number of possible games), Decision complexity (number of leaf nodes in the smallest decision tree for initial position), Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position), Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large).
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas. A (fully) quantified Boolean formula is a formula in quantified propositional logic (also known as Second-order propositional logic) where every variable is quantified (or bound), using either existential or universal quantifiers, at the beginning of the sentence. Such a formula is equivalent to either true or false (since there are no free variables).
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH.
It is well known that hyperedge-replacement grammars can generate NP-complete graph languages even under seemingly harsh restrictions. This means that the parsing problem is difficult even in the non-uniform setting, in which the grammar is considered to b ...
This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control ...
Logic synthesis is a key component of digital design and modern EDA tools; it is thus an essential instrument for the design of leading-edge chips and to push the limits of their performance. In the last decades, the electronic circuits community has evolv ...