Adaptively learning probabilistic deterministic automata from data streams

Markovian models with hidden state are widely-used formalisms for modeling sequential phenomena. Learnability of these models has been well studied when the sample is given in batch mode, and algorithms with PAC-like learning guarantees exist for specific classes of models such as Probabilistic Deterministic Finite Automata (PDFA). Here we focus on PDFA and give an algorithm for inferring models in this class in the restrictive data stream scenario: Unlike existing methods, our algorithm works incrementally and in one pass, uses memory sublinear in the stream length, and processes input items in amortized constant time. We also present extensions of the algorithm that (1) reduce to a minimum the need for guessing parameters of the target distribution and (2) are able to adapt to changes in the input distribution, relearning new models when needed. We provide rigorous PAC-like bounds for all of the above. Our algorithm makes a key usage of stream sketching techniques for reducing memory and processing time, and is modular in that it can use different tests for state equivalence and for change detection in the stream.     

The equivalence problem for real-time strict deterministic pushdown automata

A comparison method is described for a pair of real-time strict deterministic pushdown automata, capable of deciding their equivalence.Translated from Kibernetika, No. 5, pp. 14–25, September–October, 1989.     

Efficiently processing deterministic approximate aggregation query on massive data

Financial distress prediction is very important to financial institutions who must be able to make critical decisions regarding customer loans. Bankruptcy prediction and credit scoring are the two main aspects considered in financial distress prediction. To assist in this determination, thereby lowering the risk borne by the financial institution, it is necessary to develop effective prediction models for prediction of the likelihood of bankruptcy and estimation of credit risk. A number of financial distress prediction models have been constructed, which utilize various machine learning techniques, such as single classifiers and classifier ensembles, but improving the prediction accuracy is the major research issue. In addition, aside from improving the prediction accuracy, there have been very few studies that specifically consider lowering the Type I error. In practice, Type I errors need to receive careful consideration during model construction because they can affect the cost to the financial institution. In this study, we introduce a classifier ensemble approach designed to reduce the misclassification cost. The outputs produced by multiple classifiers are combined by utilizing the unanimous voting (UV) method to find the final prediction result. Experimental results obtained based on four relevant datasets show that our UV ensemble approach outperforms the baseline single classifiers and classifier ensembles. Specifically, the UV ensemble not only provides relatively good prediction accuracy and minimizes Type I/II errors, but also produces the smallest misclassification cost.     

Complementing deterministic tree-walking automata

We consider various kinds of deterministic tree-walking automata, with and without pebbles, over ranked and unranked trees. For each such kind of automata we show that there is an equivalent one which never loops. The main consequence of this result is the closure under complementation of the various types of automata we consider with a focus on the number of pebbles used in order to complement the automata.     

From LTL to deterministic automata

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula \(\varphi \). The automaton is the product of a co-Büchi automaton for \(\varphi \) and an array of Rabin automata, one for each \({\mathbf {G}}\)-subformula of \(\varphi \). The Rabin automaton for \({\mathbf {G}}\psi \) is in charge of recognizing whether \({\mathbf {F}}{\mathbf {G}}\psi \) holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed to standard procedures based on Safra’s determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.     

On stateless deterministic restarting automata

The transitions of a stateless automaton do not depend on internal states but solely on the symbols currently scanned by its head accessing the input and memory. We investigate stateless deterministic restarting automata that, after executing a rewrite step, continue to read their tape before performing a restart. Even the weakest class thus obtained contains the regular languages properly. The relations between different classes of stateless automata as well as between stateless automata and the corresponding types of automata with states are investigated, and it is shown that the language classes defined by the various types of deterministic stateless restarting automata without auxiliary symbols are anti-AFLs that are not even closed under reversal.     

Construction of minimal deterministic finite automata from biological motifs

Deterministic finite automata (DFAs) are constructed for various purposes in computational biology. Little attention, however, has been given to the efficient construction of minimal DFAs. In this article, we define simple non-deterministic finite automata (NFAs) and prove that the standard subset construction transforms NFAs of this type into minimal DFAs. Furthermore, we show how simple NFAs can be constructed from two types of pattern popular in bioinformatics, namely (sets of) generalized strings and (generalized) strings with a Hamming neighborhood.     

Equivalence of deterministic pushdown automata revisited

This paper briefly analyzes main ideas underlying the comparison algorithm that made it possible to prove the equivalence of deterministic pushdown automata. An example of using this algorithm is presented. The relationship of this algorithm with other results in this area is shown. Moreover, the decidability of problems associated with some classes of formal grammars is established. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 24–39, March–April 2007.     

From Emerson-Lei automata to deterministic,limit-deterministic or good-for-MDP automata

Innovations in Systems and Software Engineering - The topic of this paper is the determinization problem of $$omega $$ -automata under the transition-based Emerson-Lei acceptance (called TELA),...     

On real-time cellular automata and trellis automata

Summary It is shown that f(n)-time one-way cellular automata are equivalent to f(n)-time trellis automata, the real-time one-way cellular automata languages are closed under reversal, the 2n-time one-way cellular automata are equivalent to real-time cellular automata and the latter are strictly more powerful than the real-time one-way cellular automata.This work has been done during the second author's visit at the University of Paris and during both authors' visit at the Institute für Informationsverarbeitung Graz, Austria     

Amount of nonconstructivity in deterministic finite automata

When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P. Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L.E.J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was “nonconstructive arguments have no value for mathematics”. However, P. Erdös got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. The author (Freivalds, 2008) [10] showed that nonconstructive methods in coding theory are related to the notion of Kolmogorov complexity.We study the problem of the quantitative characterization of the amount of nonconstructiveness in nonconstructive arguments. We limit ourselves to computation by deterministic finite automata. The notion of nonconstructive computation by finite automata is introduced. Upper and lower bounds of nonconstructivity are proved.     

Quasi-rocking real-time pushdown automata

A pushdown automaton (PDA) is quasi-rocking if it preserves the stack height for no more than a bounded number of consecutive moves. Every PDA can be transformed into an equivalent one that is quasi-rocking and real-time and every finite-turn (one-turn) PDA can be transformed into an equivalent one that is quasi-rocking or real-time. The quasi-rocking [quasi-rocking in the increasing mode, and quasi-rocking in the decreasing mode] real-time restriction in finite-turn (one-turn) PDAs coincides with the double Greibach [reverse Greibach, and Greibach] form in nonterminal-bounded (linear) context-free grammars. This provides complete grammatical characterizations of quasi-rocking and/or real-time (finite-turn and one-turn) PDAs and, together with known relations and other relations proved in the present paper, yields an extended hierarchy of PDA languages. Basic decision properties for PDAs can be stated in stronger forms by using the quasi-rocking and real-time restrictions and their undecidability/decidability status rests on the way PDAs quasi-rock.