Concepts inEffective characterizations of tree logics
Mathematical logic
Mathematical logic (also known as symbolic logic) is a subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
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Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic has these variables as well as additional variables that range over sets of individuals.
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Well-formed formula
In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language. A formal language can be considered to be identical to the set containing all and only its formulas. A formula is a syntactic formal object that can be informally given a semantic meaning.
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L (complexity)
In computational complexity theory, L (also known as LSPACE) is the complexity class containing decision problems which can be solved by a deterministic Turing machine using a logarithmic amount of memory space. Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags and many basic logspace algorithms use the memory in this way.
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Tree automaton
A tree automaton is a type of state machine. Tree automata deal with tree structures, rather than the strings of more conventional state machines. The following article deals with branching tree automata, which correspond to regular languages of trees. For a different notion of tree automaton, see tree walking automaton. As with classical automata, finite tree automata (FTA) can be either a deterministic automaton or not.
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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols. The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed; frequently it is required to be finite. The strings formed from this alphabet are called words, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.
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