Concepts inXPath satisfiability in the presence of DTDs
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified with the truth function that takes truth to falsity and vice versa.
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Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer. A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns yes.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. In this context, a computational problem is understood to be a task that is in principle amenable to being solved by a computer (which basically means that the problem can be stated by a set of mathematical instructions).
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NP-complete
In computational complexity theory, the complexity class NP-complete (abbreviated NP-C or NPC) is a class of decision problems. A decision problem L is NP-complete if it is in the set of NP problems so that any given solution to the decision problem can be verified in polynomial time, and also in the set of NP-hard problems so that any NP problem can be converted into L by a transformation of the inputs in polynomial time.
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Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.
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PSPACE
In computational complexity theory, PSPACE is the set of all decision problems which can be solved by a Turing machine using a polynomial amount of space.
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In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time O(2) for some polynomial p(n), and unlimited space. In terms of NTIME, An important set of NEXPTIME-complete problems relates to succinct circuits. Succinct circuits are simple machines used to describe graphs in exponentially less space.
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