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Efficient static analysis of XML paths and types

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Deterministic finite automaton

In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run.

Finite-state transducer

A finite-state transducer (FST) is a finite-state machine with two memory tapes, following the terminology for Turing machines: an input tape and an output tape. This contrasts with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton (FSA) that maps between two sets of symbols. An FST is more general than an FSA. An FSA defines a formal language by defining a set of accepted strings, while an FST defines relations between sets of strings.

Alternating finite automaton

In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into existential and universal transitions. For example, let A be an alternating automaton. For an existential transition , A nondeterministically chooses to switch the state to either or , reading a. Thus, behaving like a regular nondeterministic finite automaton. For a universal transition , A moves to and , reading a, simulating the behavior of a parallel machine.

Tree (graph theory)

In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree.

XPath

XPath (XML Path Language) is an expression language designed to support the query or transformation of XML documents. It was defined by the World Wide Web Consortium (W3C) in 1999, and can be used to compute values (e.g., strings, numbers, or Boolean values) from the content of an XML document. Support for XPath exists in applications that support XML, such as web browsers, and many programming languages. The XPath language is based on a tree representation of the XML document, and provides the ability to navigate around the tree, selecting nodes by a variety of criteria.

Circuit complexity

In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circuit complexity of a recursive language that is decided by a uniform family of circuits (see below). Proving lower bounds on size of Boolean circuits computing explicit Boolean functions is a popular approach to separating complexity classes.

XML schema

An XML schema is a description of a type of XML document, typically expressed in terms of constraints on the structure and content of documents of that type, above and beyond the basic syntactical constraints imposed by XML itself. These constraints are generally expressed using some combination of grammatical rules governing the order of elements, Boolean predicates that the content must satisfy, data types governing the content of elements and attributes, and more specialized rules such as uniqueness and referential integrity constraints.

Static program analysis

In computer science, static program analysis (or static analysis) is the analysis of computer programs performed without executing them, in contrast with dynamic program analysis, which is performed on programs during their execution. The term is usually applied to analysis performed by an automated tool, with human analysis typically being called "program understanding", program comprehension, or code review. In the last of these, software inspection and software walkthroughs are also used.

Classical logic

Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Each logical system in this class shares characteristic properties: Law of excluded middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and idempotency of entailment Commutativity of conjunction De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.

XSLT

XSLT (Extensible Stylesheet Language Transformations) is a language originally designed for transforming XML documents into other XML documents, or other formats such as HTML for web pages, plain text or XSL Formatting Objects, which may subsequently be converted to other formats, such as PDF, PostScript and PNG. Support for JSON and plain-text transformation was added in later updates to the XSLT 1.0 specification. the most recent stable version of the language is XSLT 3.0, which achieved Recommendation status in June 2017.