E. M. Gold. Complexity of automaton identification from given data. Information and Control, 37(3):302--320, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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....fi rm 26 March 1998 Communicated by T. Asano Abstract We show that the problems to find the smallest acyclic DFA and OBDD with a fixed order of variables that are consistent with given sets of positive and negative examples are not approximable in polynomial time within worst case factors n 1 28 and tll 21 respectively, with the input size n unless P: NP. 1998 Elsevier Science B.V. All rights reserved Keywords. Finite state machine minimizatinn; Approximation; Combinatorial problems; Computational complexity: Data structures 1. Introduction The minimum consistency problem for ....
....that the problems to find the smallest acyclic DFA and OBDD with a fixed order of variables that are consistent with given sets of positive and negative examples are not approximable in polynomial time within worst case factors n 1 28 and tll 21 respectively, with the input size n unless P: NP. 1998 Elsevier Science B.V. All rights reserved Keywords. Finite state machine minimizatinn; Approximation; Combinatorial problems; Computational complexity: Data structures 1. Introduction The minimum consistency problem for deterministic finite automata (DFAs) is, given two sets of strings as ....
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E.M. Gold, Complexity of automaton identification from given data, Inform. and Control 37 (1978) 3(/2-320.
Efficient Ambiguity Detection in C-NFA: A Step Towards the.. - Coste, Fredouille (Correct)
....(NFA) from given positive and negative samples. This problem has been extensively studied for the inference of deterministic automata (DFA) for which state merging algorithms have been proven efficient [OG92, Lan92, CN97, LPP98, OS98] Whereas DFA are polynomially identifiable from given data [Gol78, dlH97], this result does not hold for NFA [dlH97] In contrast, it is well known that there exist languages such that their representation by DFA requires an exponential number of states with respect to the NFA representation. Considering the inference of NFA instead of DFA allows therefore to obtain ....
Gold (E. M.). -- Complexity of automaton identification from given data. Information and Control, vol. 37, 1978, pp. 302 -- 320.
Towards a General Theory of Topological Maps - Remolina, Kuipers (2002) (4 citations) (Correct)
....the set of experiences in Figure 3b. Notice that the causal and view graphs associated with the experiences in Figure 3a are isomorphic. The problem of distinguishing environment states by outputs (views) and inputs (actions) has been studied in the framework of automata theory [Angluin, 1978, Gold, 1978, Rivest and Schapire, 1987, Basye et al. 1995] In this framework, the problem we address is the one of finding the minimum automaton (w.r.t. the number of states) consistent with a given set of input output pairs. Without any particular assumptions about the environment or the agent s ....
....is the one of finding the minimum automaton (w.r.t. the number of states) consistent with a given set of input output pairs. Without any particular assumptions about the environment or the agent s perceptual abilities, the problem of finding this smallest automaton is NP complete ( Angluin, 1978, Gold, 1978] 5 Topological maps Actions in the causal theory convey patterns of experience but not spatial configuration. Spatial configuration is considered by the topological theory where actions are categorized into two classes: turns and travels. Turns and travels are explained by a new ontology, ....
E. Mark Gold. Complexity of automaton identification from given sets. Information and Control, 37:302--320, 1978.
Residual Finite State Automata - Denis, Lemay, Terlutte (2002) (Correct)
....On the other hand, inference algorithms try to detect properties of the target language from properties of some of its examples in order to build some representation of it. However, it has been shown that regular languages can be polynomially identified from given data using DFAs representations [7, 8] but that they cannot be identified in the same conditions using NFAs representations. In consequence, languages as simple as cannot be infered efficiently by inference algorithms using DFAs representations and NFAs representations cannot be used. Hence, it is a natural goal to look for ....
....infer efficiently (a representation of) a regular language from a finite set of examples of this language. Some positive results can be proved when regular languages are represented by DFAs. For example, it has been shown that Regular Languages represented by DFAs can be infered from given data ([7, 8]) In this framework, classical inference algorithms such as RPNI [13] need a polynomial number of examples relatively to the size of the minimal DFA that recognizes the language to be infered. So, regular languages as simple as cannot be infered efficiently using these algorithms. Hence, it ....
Gold, E.: Complexity of Automaton Identification from Given Data, Inform. Control, 37, 1978, 302--320.
On Sufficient Conditions to Identify in the Limit Classes of.. - Higuera, Oncina (2002) (Correct)
....generating language L. Let Other characterisations are possible, but lead to the same class. class of grammars, S is the set of all samples of languages that can be generated by grammars in G. Di#erent learning paradigms have been examined and used in the literature of machine learning [Val84,Gol78]. We will use identification in the limit from polynomial time and data [dlH97] as our learning model. Definition 1. A class of grammars is identifiable in the limit from polynomial time and data if there exist two polynomials p( and q( and an algorithm such that: 1. for each grammar G in ....
E. M. Gold. Complexity of automaton identification from given data. Information and Control, 37:302--320, 1978.
Inferring Deterministic Linear Languages - Higuera, Oncina (2002) (Correct)
.... have been examined and used in the literature of machine learning, but in the case of grammatical inference some of these: are too hard (no reasonable class can be learned) PAC learning for instance [19] are too easy (nearly anything can be learned) identification in the limit [20]. Based on identification in the limit, we will use identification in the limit from polynomial time and data [6] as our learning model. Learning from queries [13] or simple PAC learning [21] are alternative frameworks. It should be noticed that if a class of grammars is identifiable in the limit ....
....( u ) # . 4 Learning DL grammars As DL languages admit a small canonical form it will be su#cient to have an algorithm that can learn this type of canonical form, at least when a characteristic set is provided. In doing so we are following the type of proof used to prove learnability of dfa [20, 1]. Definition 12. Let L be a DL language, and # a length lexicographic order relation over # # , the shortest prefix set of L is defined as Sp L = x # Pr(L) x # y Note that, in a canonical grammar, we have a one to one relation between strings in Sp and non terminals of the grammar. ....
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Gold, E.: Complexity of automaton identification from given data. Information and Control 37 (1978) 302--320
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E. M. Gold. Complexity of automaton identification from given data. Inform. Control, 37:302--320, 1978.
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E.M. Gold. Complexity of Automaton Identification from Given Data. Information and Control, 37(3):302--320, 1978.
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E.M. Gold. "Complexity of automaton identification from given data", Information and Control 37 (1978), 302-320.
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