Concepts inXPath satisfiability in the presence of DTDs
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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XPath
XPath, the XML Path Language, is a query language for selecting nodes from an XML document. In addition, XPath may be used to compute values from the content of an XML document. XPath was defined by the World Wide Web Consortium (W3C) .
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Document Type Definition
A Document Type Definition (DTD) is a set of markup declarations that define a document type for an SGML-family markup language. A DTD uses a terse formal syntax that declares precisely which elements and references may appear where in the document of the particular type, and what the elements¿ contents and attributes are. A DTD can also declare entities which may be used in the instance document. XML uses a subset of SGML DTD.
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NEXPTIME
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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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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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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