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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 (q, a, q_1 \vee q_2), ''A'' nondeterministically chooses to switch the state to either q_1 or q_2, reading ''a''. Thus, behaving like a regular nondeterministic finite automaton. * For a universal transition (q, a, q_1 \wedge q_2), ''A'' moves to q_1 and q_2, reading ''a'', simulating the behavior of a parallel machine. Note that due to the universal quantification a run is represented by a run ''tree''. ''A'' accepts a word ''w'', if there ''exists'' a run tree on ''w'' such that ''every'' path ends in an accepting state. A basic theorem states that any AFA is equivalent to a deterministic finite automaton (DFA), hence AFAs accept exactly the regular languages. An alternative model which is frequently used is the one where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write tuples by listing the elements within parentheses "" and separated by a comma and a space; for example, denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "nbsp; or angle brackets "⟨ ⟩". Braces "" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term ''tuple'' can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PSPACE-complete
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. Theory 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 tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Language
In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1''k'', where "1" can be any fixed symbol. For example, the language is unary, as is the language . The complexity class of all such languages is sometimes called TALLY. The name "unary" comes from the fact that a unary language is the encoding of a set of natural numbers in the unary numeral system. Since the universe of strings over any finite alphabet is a countable set, every language can be mapped to a unique set A of natural numbers; thus, every language has a ''unary version'' . Conversely, every unary language has a more compact binary version, the set of binary encodings of natural numbers ''k'' such that 1''k'' is in the language. Since complexity is usually measured in terms of the length of the input string, the unary version of a language can be "easier" than the original language. For example, if a language can be recognized i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-complete
In computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis of: * which problems are difficult to parallelize effectively, * which problems are difficult to solve in limited space. specifically when stronger notions of reducibility than polytime-reducibility are considered. The specific type of reduction used varies and may affect the exact set of problems. Generically, reductions stronger than polynomial-time reductions are used, since all languages in P (except the empty language and the language of all strings) are P-complete under polynomial-time reductions. If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors, then all P-complete problems lie outside NC and so cannot be effecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word (formal Languages)
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Larry Stockmeyer
Larry Joseph Stockmeyer (1948 – 31 July 2004) was an American computer scientist. He was one of the pioneers in the field of computational complexity theory, and he also worked in the field of distributed computing. He died of pancreatic cancer. Career * 1972: BSc in mathematics, Massachusetts Institute of Technology. * 1972: MSc in electrical engineering, Massachusetts Institute of Technology. * 1974: PhD in computer science, Massachusetts Institute of Technology. ** Supervisor: Albert R. Meyer. * 1974–1982: IBM Research, Thomas J. Watson Research Center, Yorktown Heights, NY. * 1982–November 2003: IBM Research, Almaden Research Center, San Jose, CA. * October 2002–2004: University of California, Santa Cruz, Computer Science Department – Research Associate. Recognition * 1996: Fellow of the Association for Computing Machinery: "For several fundamental contributions to computational complexity theory, which have significantly affected the course of this field. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dexter Kozen
Dexter Campbell Kozen (born December 20, 1951) is an American theoretical computer scientist. He is Joseph Newton Pew, Jr. Professor in Engineering at Cornell University. He received his B.A. from Dartmouth College in 1974 and his PhD in computer science in 1977 from Cornell University, where he was advised by Juris Hartmanis. He advised numerous Ph.D. students. He is a Fellow of the Association for Computing Machinery, a Guggenheim Fellow, and has received an Outstanding Innovation Award from IBM Corporation. He has also been named Faculty of the Year by the Association of Computer Science Undergraduates at Cornell. Dexter Kozen was one of the first professors to receive the honor of a professorship at The Radboud Excellence Initiative at Radboud University Nijmegen in the Netherlands. He is known for his work at the intersection of logic and complexity. He is one of the fathers of dynamic logic and developed the version of the modal μ-calculus most used today. Moreover, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ashok K
Ashoka (, ; also ''Asoka''; 304 – 232 BCE), popularly known as Ashoka the Great, was the third emperor of the Maurya Empire of Indian subcontinent during to 232 BCE. His empire covered a large part of the Indian subcontinent, stretching from present-day Afghanistan in the west to present-day Bangladesh in the east, with its capital at Pataliputra. A patron of Buddhism, he is credited with playing an important role in the spread of Buddhism across ancient Asia. Much of the information about Ashoka comes from his Brahmi edicts, which are among the earliest long inscriptions of ancient India, and the Buddhist legends written centuries after his death. Ashoka was son of Bindusara, and a grandson of the dynasty's founder Chandragupta. During his father's reign, he served as the governor of Ujjain in central India. According to some Buddhist legends, he also suppressed a revolt in Takshashila as a prince, and after his father's death, killed his brothers to ascend t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternating Tree Automaton
In automata theory, an alternating tree automaton (ATA) is an extension of nondeterministic tree automaton as same as alternating finite automaton extends nondeterministic finite automaton (NFA). Computational complexity The emptiness problem (deciding whether the language of an input ATA is empty) and the universality problem for ATAs are EXPTIME-complete In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable by a deterministic Turing machine in exponential time, i.e., in O(2''p''(''n'')) time, whe ....H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison et M. Tommasi, ''Tree Automata Techniques and Applications'(Theorem 7.5.1 and subsequent remark) The membership problem (testing whether an input tree is accepted by an input AFA) is in PTIME. References Automata (computation) {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nondeterministic Finite Automaton
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if * each of its transitions is ''uniquely'' determined by its source state and input symbol, and * reading an input symbol is required for each state transition. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is ''not'' a DFA, but not in this article. Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. Like DFAs, NFAs only recognize regular languages. NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott, who also showed their equivalence to DFAs. NFAs are used in the implementation of regular expressions: Thompson's construction is an algorithm for compiling a regular expression to an NFA that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. As with classical automata, finite tree automata (FTA) can be either a deterministic automaton or not. According to how the automaton processes the input tree, finite tree automata can be of two types: (a) bottom up, (b) top down. This is an important issue, as although non-deterministic (ND) top-down and ND bottom-up tree automata are equivalent in expressive power, deterministic top-down automata are strictly less powerful than their deterministic bottom-up counterparts, because tree properties specified by deterministic top-down tree automata can only depend on path properties. (Deterministic bottom-up tree automata are as powerful as ND tree automata.) Definitions A bottom-up finite tree automaton over ''F'' is defined as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
