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221
Computing With FirstOrder Logic
, 1995
"... We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtaine ..."
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Cited by 53 (13 self)
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We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The fixpoint query computes an equivalence relation on tuples which is a congruence with respect to the rest of the computation. The same technique is used to show that equivalence of tuples and structures with respect to FO formulas with bounded number of variables is definable in fixpoint. Generalizing fixpoint and while, we consider more powerful languages which model arbitrary computation interacting with a database using a finite set of FO queries. Such computation is modeled by a relational machine...
Fast Text Searching for Regular Expressions or Automaton Searching on Tries
"... We present algorithms for efficient searching of regular expressions on preprocessed text, using a Patricia tree as a logical model for the index. We obtain searching algorithms that run in logarithmic expected time in the size of the text for a wide subclass of regular expressions, and in subline ..."
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Cited by 49 (6 self)
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We present algorithms for efficient searching of regular expressions on preprocessed text, using a Patricia tree as a logical model for the index. We obtain searching algorithms that run in logarithmic expected time in the size of the text for a wide subclass of regular expressions, and in sublinear expected time for any regular expression. This is the first such algorithm to be found with this complexity.
Incremental Construction of Minimal Acyclic Finite State Automata and Transducers
, 1998
"... In this paper, we describe a new method for constructing mi, lmal, determin istic, acyclic finite state automata and transducers. Traditional methods consist of two steps. The first one is to construct a trie, the second one  to perform minimization. Our approach is to construct an automaton i ..."
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Cited by 42 (4 self)
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In this paper, we describe a new method for constructing mi, lmal, determin istic, acyclic finite state automata and transducers. Traditional methods consist of two steps. The first one is to construct a trie, the second one  to perform minimization. Our approach is to construct an automaton in a single step by adding new strings one by one and minjmizin the resulting automaton onthefly. We present a general algorithm as well as a specialization that relies upon the lexicographical sorting of the input strings.
Analysis of Dynamical Recognizers
 NEURAL COMPUTATION
, 1996
"... Pollack (1991) demonstrated that secondorder recurrent neural networks can act as dynamical recognizers for formal languages when trained on positive and negative examples, and observed both phase transitions in learning and IFSlike fractal state sets. Followon work focused mainly on the extra ..."
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Cited by 33 (5 self)
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Pollack (1991) demonstrated that secondorder recurrent neural networks can act as dynamical recognizers for formal languages when trained on positive and negative examples, and observed both phase transitions in learning and IFSlike fractal state sets. Followon work focused mainly on the extraction and minimization of a finite state automaton (FSA) from the trained network. However, such networks are capable of inducing languages which are not regular, and therefore not equivalenttoany FSA. Indeed, it may be simpler for a small network to fit its training data by inducing such a nonregular language. But when is the network's language not regular? In this paper, using a low dimensional network capable of learning all the Tomita data sets, we present an empirical method for testing whether the language induced by the network is regular or not. We also provide a detailed "machine analysis of trained networks for both regular and nonregular languages.
On the Power of NumberTheoretic Operations with Respect to Counting
 IN PROCEEDINGS 10TH STRUCTURE IN COMPLEXITY THEORY
, 1995
"... We investigate function classes h#Pi f which are defined as the closure of #P under the operation f and a set of known closure properties of #P, e.g. summation over an exponential range. First, we examine operations f under which #P is closed (i.e., h#Pi f = #P) in every relativization. We obtain t ..."
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Cited by 32 (9 self)
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We investigate function classes h#Pi f which are defined as the closure of #P under the operation f and a set of known closure properties of #P, e.g. summation over an exponential range. First, we examine operations f under which #P is closed (i.e., h#Pi f = #P) in every relativization. We obtain the following complete characterization of these operations: #P is closed under f in every relativization if and only if f is a finite sum of binomial coefficients over constants. Second, we characterize operations f with respect to their power in the counting context in the unrelativized case. For closure properties f of #P, we have h#Pi f = #P. The other end of the range is marked by operations f for which h#Pi f corresponds to the counting hierarchy. We call these operations counting hard and give general criteria for hardness. For many operations f we show that h#Pi f corresponds to some subclass C of the counting hierarchy. This will then imply that #P is closed under f if and only if ...
On Balanced vs. Unbalanced Computation Trees
"... A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial time machines. Jenner, McKenzie, and Th'erien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether consi ..."
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Cited by 29 (7 self)
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A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial time machines. Jenner, McKenzie, and Th'erien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether considering balanced or unbalanced trees makes any difference. For a number of leaf language classes, coincidence of both models was shown, but for the very prominent example of leaf language classes from the alternating logarithmic time hierarchy the question was left open. It was only proved that in the balanced case these classes exactly characterize the classes from the polynomial time hierarchy. Here, we show that balanced trees apparently make a difference: In the unbalanced case, a class from the logarithmic time hierarchy characterizes the corresponding class from the polynomial time hierarchy with a PPoracle. Along the way, we get an interesting normal form for PP computations.
Randomness, Interactive Proofs and . . .
 APPEARS IN THE UNIVERSAL TURING MACHINE: A HALFCENTURY SURVEY, R. HERKEN ED.
, 1987
"... Recent approaches to the notions of randomness and proofs are surveyed. The new notions differ from the traditional ones in being subjective to the capabilities of the observer rather than reflecting "ideal " entities. The new notion of randomness regards probability distributions as equal if they c ..."
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Cited by 29 (6 self)
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Recent approaches to the notions of randomness and proofs are surveyed. The new notions differ from the traditional ones in being subjective to the capabilities of the observer rather than reflecting "ideal " entities. The new notion of randomness regards probability distributions as equal if they cannot be told apart by efficient procedures. This notion is constructive and is suited for many applications. The new notion of a proof allows the introduction of the notion of zeroknowledge proofs: convincing arguments which yield nothing but the validity of the assertion. The new approaches to randomness and proofs are based on basic concepts and results from the theory of resourcebounded computation. In order to make the survey as accessible as possible, we have presented elements of the theory of resource bounded computation (but only to the extent required for the description of the new approaches). This survey is not intended to provide an account of the more traditional approaches to randomness (e.g. Kolmogorov Complexity) and proofs (i.e. traditional logic systems). Whenever these approaches are described it is only in order to confront them with the new approaches.
Lexicographical Indices for Text: Inverted files vs. PAT trees
, 1991
"... We survey two indices for text, with emphasis on Pat arrays (also called suffix arrays). A Pat array is an index based on a new model of text which does not use the concept of word and does not need to know the structure of the text. to appear in Information Retrieval: Data Structures and Algori ..."
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Cited by 23 (0 self)
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We survey two indices for text, with emphasis on Pat arrays (also called suffix arrays). A Pat array is an index based on a new model of text which does not use the concept of word and does not need to know the structure of the text. to appear in Information Retrieval: Data Structures and Algorithms, R.A. BaezaYates and W. Frakes, eds., PrenticeHall. 1 1 Introduction Text searching methods may be classified as lexicographical indices (indices that are sorted), clustering techniques, and indices based on hashing (for example, signature files [FC87]). In this report we discuss lexicographical indices, in particular, two main data structures: inverted files and Pat trees. Our aim is to build an index for the text of size similar to or smaller than the text. Briefly, the traditional model of text used in information retrieval is that of a set of documents. Each document is assigned a list of keywords (attributes), with optional relevance weights associated to each keyword. This ...
A Taxonomy of Finite Automata Minimization Algorithms
, 1993
"... This paper presents a taxonomy of finite automata minimization algorithms. Brzozowski's elegant minimization algorithm differs from all other known minimization algorithms, and is derived separately. All of the remaining algorithms depend upon computing an equivalence relation on states. We define t ..."
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Cited by 21 (4 self)
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This paper presents a taxonomy of finite automata minimization algorithms. Brzozowski's elegant minimization algorithm differs from all other known minimization algorithms, and is derived separately. All of the remaining algorithms depend upon computing an equivalence relation on states. We define the equivalence relation, the partition that it induces, and its complement. Additionally, some useful properties are derived. It is shown that the equivalence relation is the greatest fixed point of an equation, providing a useful characterization of the required computation. We derive an upperbound on the number of approximation steps required to compute the fixed point. Algorithms computing the equivalence relation (or the partition, or its complement) are derived systematically in the same framework. The algorithms include Hopcroft's, several algorithms from textbooks (including Hopcroft and Ullman's [HU79], Wood's [Wood87], and Aho, Sethi, and Ullman's [ASU86]), and several new algorith...
Approximate Matching of Network Expressions with Spacers
 Journal of Computational Biology
, 1992
"... Two algorithmic results are presented that are pertinent to the matching of patterns of interest in macromolecular sequences. The first result is an output sensitive algorithm for approximately matching network expressions, i.e., regular expressions without Kleene closure. This result generalizes th ..."
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Cited by 19 (0 self)
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Two algorithmic results are presented that are pertinent to the matching of patterns of interest in macromolecular sequences. The first result is an output sensitive algorithm for approximately matching network expressions, i.e., regular expressions without Kleene closure. This result generalizes the O (kn ) expectedtime algorithm of Ukkonen for approximately matching keywords [Ukk85]. The second result concerns the problem of matching a pattern that is a network expression whose elements are approximate matches to network expressions interspersed with specifiable distance ranges. For this class of patterns, it is shown how to determine a backtracking procedure whose order of evaluation is optimal in the sense that its expected time is minimal over all such procedures. Key words: Approximate Match, Backtracking, Network Expression, Proximity Search January 16, 1992 Department of Computer Science The University of Arizona Tucson, Arizona 85721 *This work was supported in part by the ...