Input Word Research Articles

One-Way Jumping Finite Automata

We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

Scope-Bounded Pushdown Languages

We study the formal language theory of multistack pushdown automata (MPA) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped MPA). We show that scoped MPA are indeed a robust model of computation, by focusing on the corresponding theory of visibly MPA (MVPA). We prove the equivalence of the deterministic and nondeterministic versions and show that scope-bounded computations of an n-stack MVPA can be simulated, rearranging the input word, by using only one stack. These results have some interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and the effective semilinearity of the Parikh image (Parikh's theorem). As a further contribution, we give a logical characterization and compare the expressiveness of the scope-bounded restriction with other MVPA classes from the literature. To the best of our knowledge, scoped MVPA languages form the largest class of formal languages accepted by MPA that enjoys all the above nice properties.

Conjugacy in Baumslag’s Group, Generic Case Complexity, and Division in Power Circuits

The conjugacy problem asks whether two words over generators of a fixed group G are conjugated, i.e., it is the problem to decide on input words x, y whether there exists z such that $$zx z^{-1} =y$$zxz-1=y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the conjugacy problem for two prominent groups: the Baumslag---Solitar group $$\mathbf{{BS}}_{1,2}$$BS1,2 and the Baumslag group $${\mathbf{{G}}}_{1,2}$$G1,2 (also known as Baumslag---Gersten group). The conjugacy problem in $${\mathbf{{BS}}}_{1,2}$$BS1,2 is complete for the circuit class $$\mathsf {TC}^0$$TC0. To the best of our knowledge $${\mathbf{{BS}}}_{1,2}$$BS1,2 is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group $${\mathbf{{G}}}_{1,2}$$G1,2 is an HNN-extension of $${\mathbf{{BS}}}_{1,2}$$BS1,2. Hence, decidability of the conjugacy problem in $$\mathbf{{G}}_{1,2}$$G1,2 outside the so-called black hole follows from Borovik et al. (Int J Algebra Comput 17(5/6):963---997, 2007). Decidability everywhere is due to Beese. Moreover, he showed exponential time for the set of elements which cannot be conjugated into $$\mathbf{{BS}}_{1,2}$$BS1,2 (Beese 2012). Here we improve Beese's result in two directions by showing that the conjugacy problem in $${\mathbf{{G}}}_{1,2}$$G1,2 can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs, conjugacy in $${\mathbf{{G}}}_{1,2}$$G1,2 can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in $${\mathbf{{G}}}_{1,2}$$G1,2 by reducing the divisibility problem in power circuits to the conjugacy problem in $${\mathbf{{G}}}_{1,2}$$G1,2. The complexity of the divisibility problem in power circuits is an open and interesting problem in integer arithmetic. We conjecture that it cannot be solved in elementary time because we can show that it cannot be solved in elementary time by calculating modulo values in power circuits.

Analysis of Quarter Rounds of Salsa and Chacha Core and Proposal of an Alternative Design to Maximize Diffusion

Background/Objectives: Salsa and ChaCha are commonly used encryption primitives. Both Salsa and ChaCha core use Quarter round as its core function. The objective of the paper is to analyze the diffusion property of Quarter round of both these algorithms and propose an alternative design named Modified ChaCha Core (MCC). Methods: The Quarter round functions of all these three algorithms are compared using the diffusion matrices that reflect change in output words with a small change in input words. For each algorithm we generated more than a million diffusion matrices depending on the possible permutations of rotations constants used in Quarter round. Findings: Results of our experiment reflected that for Salsa and ChaCha core, there are high number of alternative rotation constants that generate more diffusion than the rotation constants prescribed by the authors. The comparison of diffusion matrices of all three competing structures also concluded that quarter round of MCC exhibits more diffusion than Quarter round of Salsa and ChaCha and it does so in lesser operations. Applications: MCC core; the design proposed in this paper, may be used to generate stream ciphers or may be used to generate collision resistant compression function for a cryptographic hash algorithm. Keywords: ChaCha, Diffusion, Modified ChaCha, MCC, Salsa, Stream Ciphers

Sequence Labeling for Cognate Production

We propose a sequence labeling approach to cognate production based on the orthography of the words. Our approach leverages the idea that orthographic changes represent sound correspondences to a fairly large extent. Given an input word in language L1, we seek to determine its cognate pair in language L2. To this end, we employ a sequential model which captures the intuition that orthographic changes are highly dependent on the context in which they occur. We apply our method on two pairs of languages. Finally, we investigate how second language learners perceive the orthographic changes from their mother tongue to the language they learn.

Behavior of finite-nonstationary deterministic automata in a fuzzy environment

The paper presents a method of finding optimal control of generalized deterministic abstract automaton, the structure of which is given by an arbitrary finite graph in a fuzzy environment. The control is found in order to achieve a fuzzy goal, which is given as a fuzzy set in any fixed finite vertex of the automaton structural graph. The problem solution is divided into two stages. The first stage provides the greatest possible degree of achieving the fuzzy goal depending on the path from the initial graph vertex to the fixed one, while the second stage makes it possible to construct a set of input words that ensure the achievement of this goal on the selected path. The conclusion presents an example of the application of the proposed method for constructing a regular expression of control sequences for the given abstract finite-nonstationary deterministic automaton.

Using Computing with Words for Selecting Projects in Field of Fuel Consumption Reduction

Background/Objectives: Nowadays, most organizations acknowledge the role and significance of different energy resources in the supply of present and future needs. As a result, they make sizeable investments and undertake extensive research on strategy and policy making as well as definition of infrastructure projects to reduce energy consumption. According to the diversity of projects and their cost of implementation, ranking the projects with different criteria is currently one of the complex problems in organizations. This paper presents a new solution based on the specific architecture of Perceptual Computer (Per-C) for project selection. Methods/Statistical Analysis: In project selection problem, decision makers express their assessment in the form of the linguistic terms that they are vague and uncertain. Using Per-C method is a new experience in project selection problems that has not been mentioned in any literature so far. The Per-C has three components: an Encoder, which maps words into IT2 FS models; a CWW engine, which operates on the input words and whose outputs are FOU(s); and a Decoder, which maps these FOU(s) into a recommendation. We used the Interval Approach (IA) for Decoding, Linguistic Weighted Average (LWA) method is used in CWW engine and Centroid method is used for Decoding. Findings and Application/Improvements: A real case study from a power plant is used to illustrate the applicability of the approach. Using Per-C method is a new experience in project selection problems that has not been mentioned in any literature so far. The results show the applicability of the proposed methodology clearly.

Infants generalize from just (the right) four words

Infants in the lab can generalize from 2min of language-like input. Given that infants might fail to fully encode so much input, how many examples do they actually need? And if infants only encode a subset of their input at one time, does generalization change when that subset supports multiple generalizations? Exp. 1 asked whether 11-month-olds generalize the relation between two consonants in a word when just four input words provided non-conflicting vs. partially conflicting support for a phonological feature-based generalization. Infants learned under both conditions, although the latter appears to be more difficult. Exp. 2 asked whether infants’ robust learning reflects a bias toward feature-based generalizations. Infants failed to generalize when input provided completely conflicting support for two generalizations. Together, the data suggest that infants are able to generalize from much less input than previously observed, but generalization depends on the specific subset of the input they encounter.

Early semantic activation in a semantic categorization task with masked primes: Cascaded or not?

The assumption that activation is cascaded implies that the semantic properties of all neighbors of the input word are activated to varying degrees. This assumption is tested using masked priming in a semantic categorization experiment, where the prime belongs to the same category as the target (a congruent prime), or to a different category (an incongruent prime). In Experiment 1, the prime was a nonword neighbor of an exemplar or non-exemplar of the category, and a clear congruence effect was produced, even though the orthographic overlap was fairly low (e.g., lucchibi-zucchini). In Experiment 2, the prime was a word neighbor (e.g., capable-cabbage), which eliminates the possibility that the prime was simply interpreted as equivalent to the nearest task-relevant word, but a congruence effect was still obtained. Experiment 3 replicated this effect. Experiments 4–6 investigated the possible role of the category using a two-alternative forced choice discrimination task, where the task was simply to guess which of two subsequently presented words was more similar in meaning to the masked word. Despite better than chance performance when the masked word was related to one of the alternatives, performance was at chance when the masked word was a neighbor of a word that was related to one of the alternatives, indicating that semantic activation is not normally cascaded. It is concluded that the categorization task fundamentally alters the way in which a masked word is processed.

The power of greedy algorithms for approximating Max-ATSP, Cyclic Cover, and superstrings

The Maximum Asymmetric Travelling Salesman Problem (Max-ATSP), which asks for a Hamiltonian path of maximum weight covering a digraph, and the Maximum Compression(Max-Comp), which, for a finite language P≔{s1,…,sp}, asks for w, a superstring of P minimising ∑si∈S|si|−|w|, are both difficult to approximate (Max-SNP hard). Solving Max-ATSP on the overlap graph of the words of P solves Max-Comp. Many approximate algorithms have been designed to improve their approximation ratios, but these are increasingly complex. Often, these rely on solving the pendant problems where the cover is made of cycles instead of single path (Max-CC and SCCS). Thus, the greedy algorithm remains an attractive solution for its simplicity and ease of implementation. Here, using the full power of subset systems, we provide a unified approach for proving simply the approximation ratios of a greedy algorithm for these four problems. In addition, we introduce two new problems dealing with the case of cyclic input words, and exhibit a greedy approximation ratio for them. The Maximum Partitioned Hamiltonian Path generalises the Maximum Asymmetric Travelling Salesman Problem when the nodes are partitioned into classes and the path must contain one element of each class. The Maximum Cyclic Compression is the natural counterpart of Maximum Compression for cyclic strings.

Quantization causes waves: Smooth finitely computable functions are affine

Every automaton (a letter-to-letter transducer) A whose both input and output alphabets are F p = {0, 1,..., p - 1} produces a 1-Lipschitz map f A from the space Z p of p-adic integers to Z p . The map fA can naturally be plotted in a unit real square I2 ⊂ R2: To an m-letter non-empty word v = γ m-1γ m-2... γ0 there corresponds a number 0.v ∈ R with base-p expansion 0.γ m-1γ m-2... γ0; so to every m-letter input word w = α m-1α m-2 ··· α0 of A and to the respective m-letter output word a(w) = β m-1β m-2 ··· β0 of A there corresponds a point (0.w; 0.a(w)) ∈ R2. Denote P(A) a closure of the point set (0.w; 0.a(w)) where w ranges over all non-empty words.We prove that once some points of P(A) constitute a C 2-smooth curve in R2, the curve is a segment of a straight line with a rational slope. Moreover, when identifying P(A) with a subset of a 2-dimensional torus T2 ∈ R3, the smooth curves from P(A) constitute a collection of torus windings which can be ascribed to complex-valued functions ψ(x, t) = e i(Ax-2πBt) (x, t ∈ R), i.e., to matter waves. As automata are causal discrete systems, the main result may serve a mathematical reasoning why wave phenomena are inherent in quantum systems: This is just because of causality principle and discreteness of matter.

Efficient Algorithm for Recognizing the Nielsen–Thurston Type of a Three–Strand Braid

We propose an efficient algorithm for recognizing the Nielsen–Thurston type of a braid in the braid group B3. The algorithm has linear complexity on the input word length. Bibliography: 11 titles. Illustrations: 5 figures.

Bigram Language Models and Reevaluation Strategy for Improved Recognition of Online Handwritten Tamil Words

This article describes a postprocessing strategy for online, handwritten, isolated Tamil words. Contributions have been made with regard to two issues hardly addressed in the online Indic word recognition literature, namely, use of (1) language models exploiting the idiosyncrasies of Indic scripts and (2) expert classifiers for the disambiguation of confused symbols. The input word is first segmented into its individual symbols, which are recognized using a primary support vector machine (SVM) classifier. Thereafter, we enhance the recognition accuracy by utilizing (i) a bigram language model at the symbol or character level and (ii) expert classifiers for reevaluating and disambiguating the different sets of confused symbols. The symbol-level bigram model is used in a traditional Viterbi framework. The concept of a character comprising multiple symbols is unique to Dravidian languages such as Tamil. This multi-symbol feature of Tamil characters has been exploited in proposing a novel, prefix-tree-based character-level bigram model that does not use Viterbi search; rather it reduces the search space for each input symbol based on its left context. For disambiguating confused symbols, a dynamic time-warping approach is proposed to automatically identify the parts of the online trace that discriminates between the confused classes. Fine classification of these regions by dedicated expert SVMs reduces the extent of confusions between such symbols. The integration of segmentation, prefix-tree-based language model and disambiguation of confused symbols is presented on a set of 15,000 handwritten isolated online Tamil words. Our results show recognition accuracies of 93.0% and 81.6% at the symbol and word level, respectively, as compared to the baseline classifier performance of 88.4% and 65.1%, respectively.

Моделирование и анализ поведения последовательных реагирующих программ

Finite state transducers extend the finite state automata to model functions on strings or lists. They may be used also as simple models of sequential reactive programs. These programs operate in the interaction with the environment permanently receiving data (requests) from it. At receiving a piece of data such program performs a sequence of actions. When certain control points are achieved a program outputs the current results of computation as a response. It is significant that different sequences of actions may yield the same result. Therefore, the basic actions of a program may be viewed as generating elements of some appropriate semigroup, and the result of computation may be regarded as the composition of actions performed by the program. This paper offers an alternative technique for the analysis of finite state transducers over semigroups. To check the equivalence of transducers and we associate with them a Labeled Transition Systems . Each path in this LTS represents all possible runs of and on the same input word. Every node of keeps track of the states of and achieved at reading some input word and the deficiency of the output words computed so far. If both transducers reach their final states and the deficiency of their outputs is nonzero then this indicates that and produce different images for the same word, and, hence, they are not equivalent. The nodes of that capture this effect are called rejecting nodes. Thus, the equivalence checking of and is reduced to checking the reachability of rejecting nodes in LTS . We show that one needs to analyze only a bounded fragment of to certify (un)reachability of rejecting nodes. The size of this fragment is polynomial of the size of and if both transducers are deterministic, and single-exponential if they are k-bounded. The same approach is applicable for checking k-valuedness of transducers over semigroups.

Assessment Criteria for Benchmarking Arabic Morphological Analyzers and Generators

Natural language processing applications are based on the morphology part. So they should meet some criteria in order to satisfy the required functionality. Assessing and evaluating of Arabic morphological systems depend on the input words and resulted output according to a predefined criteria to measure and analyze given system in order to study its weakness and strength, trying to find an Arabic morphological analyzer free from all mistakes. In this paper we developed the precise assessment criteria for Arabic morphological analyzers to be applied on a given Arabic morphological analyzers and stemming algorithms by voting, after running them on the sample documents selected as the gold standard.

Parameterized Weighted Containment

Partially specified systems and specifications are used in formal methods such as stepwise design and query checking. Existing methods consider a setting in which systems and their correctness are Boolean. In recent years, there has been growing interest and need for quantitative formal methods, where systems may be weighted and specifications may be multivalued. Weighted automata, which map input words to a numerical value, play a key role in quantitative reasoning. Technically, every transition in a weighted automaton A has a cost, and the value A assigns to a finite word w is the sum of the costs on the transitions traversed along the most expensive accepting run of A on w . We study parameterized weighted containment : given three weighted automata A , B , and C , with B being partial, the goal is to find an assignment to the missing costs in B so that we end up with B ′ for which B ′≤ C , where ≤ is the weighted counterpart of containment. We also consider a one-sided version of the problem, where only A or only C is given in addition to B , and the goal is to find a minimal assignment with which A ≤ B ′ or, respectively, a maximal one with which B ′ ≤ C . We argue that both problems are useful in stepwise design of weighted systems as well as approximated minimization of weighted automata. We show that when the automata are deterministic, we can solve the problems in polynomial time. Our solution is based on the observation that the set of legal assignments to k missing costs forms a k -dimensional polytope. The technical challenge is to find an assignment in polynomial time even though the polytope is defined by means of exponentially many inequalities. We do so by developing a divide-and-conquer algorithm based on a separation oracle for polytopes. For nondeterministic automata, the weighted setting is much more complex, and in fact even nonparameterized containment is undecidable. We are able to show positive results for variants of the problems, where containment is replaced by simulation.

Deterministic Timed Finite State Machines: Equivalence Checking and Expressive Power

There has been a growing interest in defining models of automata enriched with time. For instance, timed automata were introduced as automata extended with clocks. In this paper, we study models of timed finite state machines (TFSMs), i.e., FSMs enriched with time, which accept timed input words and generate timed output words. Here we discuss some models of TFSMs with a single clock: TFSMs with timed guards, TFSMs with timeouts, and TFSMs with both timed guards and timeouts. We solve the problem of equivalence checking for all three models, and we compare their expressive power, characterizing subclasses of TFSMs with timed guards and of TFSMs with timeouts that are equivalent to each other.

Lexicon reduction for printed Farsi subwords using pictorial and textual dictionaries

In this paper, we present a method to reduce the lexicon size of printed Farsi subwords, which utilizes the holistic shape along with the key character information to dynamically reduce the size of lexicon organized accordingly in two approaches: (1) based on the global shape description (to build a pictorial dictionary) and (2) based on constitutive character information (to build a textual dictionary). Given an input word image, the reduction procedure is accomplished in two successive stages. First, characteristic loci features are extracted and compared with the pictorial dictionary to select the candidate subwords based on their shapes similarity. The lexicon is further reduced in the second stage by determining the key character in the input image and comparing it with the textual dictionary. The key characters are defined as the ones which can be segmented and recognized rather easily and also, together with global descriptors, characterize the word image efficiently. A method for optimal selection of key characters is also proposed which is based on the mutual information of pictorial and textual dictionaries. The final candidate subwords are those sharing the same key character with the input image. The performance of the proposed method was studied experimentally on a set of 5,000 subword samples. The results obtained show a reduction rate of 97.83 % on a lexicon of 6,900 printed Farsi subwords.

E-TCAM: An Efficient SRAM-Based Architecture for TCAM

Ternary content addressable memories (TCAMs) perform high-speed search operation in a deterministic time. However, when compared with static random access memories (SRAMs), TCAMs suffer from certain limitations such as low-storage density, relatively slow access time, low scalability, complex circuitry, and higher cost. One fundamental question is that can we utilize SRAM to combine it with additional logic to achieve the TCAM functionality? This paper proposes an efficient memory architecture, called E-TCAM, which emulates the TCAM functionality with SRAM. E-TCAM logically divides the classical TCAM table along columns and rows into hybrid TCAM subtables and then maps them to their corresponding memory blocks. During search operation, the memory blocks are accessed by their corresponding subwords of the input word and a match address is produced. An example design of $$512\times 36$$ 512 × 36 of E-TCAM has been successfully implemented on Xilinx Virtex- $$5$$ 5 , Virtex- $$6$$ 6 , and Virtex- $$7$$ 7 field-programmable gate arrays (FPGAs). FPGA implementation results show that E-TCAM obtains $$33.33$$ 33.33 % reduction in block-RAMs, $$71.07$$ 71.07 % in slice registers, $$77.16$$ 77.16 % in lookup tables, $$53.54$$ 53.54 % in energy/bit/search, and offers $$63.03$$ 63.03 % improvement in speed, compared with the best available SRAM-based TCAM designs.

Smoothing of HMM parameters for efficient recognition of online handwriting

In this paper, we propose a novel approach to limited vocabulary recognition of unconstrained (mixed cursive) handwriting based on a hidden Markov model (HMM). Here, an input word sample is segmented into sub-strokes. However, instead of recognizing individual sub-strokes, we recognize the whole word sample as a basic unit. In this study, we consider both circular and linear features. The von Mises distribution is used to model circular feature components while the Gaussian distribution is used for the linear features. We implement fully connected non-homogeneous HMMs considering the enormous variability in the present handwriting style which often includes delayed strokes. Since such an HMM involves a large number of parameters, we implement a simple but novel approach to smoothing of HMM parameters to avoid possible over-fitting and poor generalization. Finally, in the proposed approach, we combine recognition results of two HMMs: one considering the input sample in the natural order and the other considering the sample in the reverse order. A major goal of the present study is to develop an efficient recognition scheme for online unconstrained handwritten words of Bangla, a popular Indic script.