State Automata Research Articles

Конечные автоматы в теории алгебраических схем программ

Algebraic models of programs considered in this paper generalize two models of programs introduced by A.A. Lyapunov and A.A. Letichevsky. The theory of these models focuses on the equivalence checking problem for program schemata which are formalization of imperative programs. We prove that this problem is decidable for a wide class of algebraic models of programs. Our decision techniques are based on the approach to the equivalence checking problem for finite state automata. The aim of this paper is to reveal this relationship.

SCESS: a WFSA-based automated simplified chinese essay scoring system with incremental latent semantic analysis

AbstractWriting in language tests is regarded as an important indicator for assessing language skills of test takers. As Chinese language tests become popular, scoring a large number of essays becomes a heavy and expensive task for the organizers of these tests. In the past several years, some efforts have been made to develop automated simplified Chinese essay scoring systems, reducing both costs and evaluation time. In this paper, we introduce a system called SCESS (automated Simplified Chinese Essay Scoring System) based on Weighted Finite State Automata (WFSA) and using Incremental Latent Semantic Analysis (ILSA) to deal with a large number of essays. First, SCESS uses ann-gram language model to construct a WFSA to perform text pre-processing. At this stage, the system integrates a Confusing-Character Table, a Part-Of-Speech Table, beam search and heuristic search to perform automated word segmentation and correction of essays. Experimental results show that this pre-processing procedure is effective, with a Recall Rate of 88.50%, a Detection Precision of 92.31% and a Correction Precision of 88.46%. After text pre-processing, SCESS uses ILSA to perform automated essay scoring. We have carried out experiments to compare the ILSA method with the traditional LSA method on the corpora of essays from the MHK test (the Chinese proficiency test for minorities). Experimental results indicate that ILSA has a significant advantage over LSA, in terms of both running time and memory usage. Furthermore, experimental results also show that SCESS is quite effective with a scoring performance of 89.50%.

Pushdown Automata in Statistical Machine Translation

This article describes the use of pushdown automata (PDA) in the context of statistical machine translation and alignment under a synchronous context-free grammar. We use PDAs to compactly represent the space of candidate translations generated by the grammar when applied to an input sentence. General-purpose PDA algorithms for replacement, composition, shortest path, and expansion are presented. We describe HiPDT, a hierarchical phrase-based decoder using the PDA representation and these algorithms. We contrast the complexity of this decoder with a decoder based on a finite state automata representation, showing that PDAs provide a more suitable framework to achieve exact decoding for larger synchronous context-free grammars and smaller language models. We assess this experimentally on a large-scale Chinese-to-English alignment and translation task. In translation, we propose a two-pass decoding strategy involving a weaker language model in the first-pass to address the results of PDA complexity analysis. We study in depth the experimental conditions and tradeoffs in which HiPDT can achieve state-of-the-art performance for large-scale SMT.

Subset Synchronization of Transitive Automata

We consider the following generalized notion of synchronization: A word is called a reset word of a subset of states of a deterministic finite automaton if it maps all states of the set to a unique state. It is known that the minimum length of such words is superpolynomial in worst cases, namely in a series of substantially nontransitive automata. We present a series of transitive binary automata with a strongly exponential minimum length. This also constitutes a progress in the research of composition sequences initiated by Arto Salomaa, because reset words of subsets are just a special case of composition sequences. Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that this holds even if we restrict the problem to transitive binary automata.

A description based on languages of the final non-deterministic automaton

The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. Under this interpretation, the different branches that can be taken at every step are ignored. However, we can also take into account the different decisions which can be made at every state, that is, the branches that can be taken, and these decisions might change the possible future behaviour. In this case, the behaviour of the automata can be described with the help of the concept of bisimilarity. This is the kind of description that is usually obtained when the automata are regarded as labelled transition systems or coalgebras.Contrarily to what happens with deterministic automata, it is not possible to describe the behaviour up to bisimilarity of states of a non-deterministic automaton by considering just the languages associated to them. In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages. As a consequence, we obtain a characterisation of bisimilarity of states of automata in terms of languages and a method to minimise non-deterministic automata with respect to bisimilarity of states. This confirms that languages can be considered as the natural objects to describe the behaviour of automata.

Learning Cover Context-Free Grammars from Structural Data

We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most l. The goal is to learn a cover context-free grammar (CCFG) with respect to l, that is, a CFG whose structural descriptions with depth at most l agree with those of the unknown CFG. We propose an algorithm, called LA l, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that LA l runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to l. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar.

A novel algorithm for the conversion of shuffle regular expressions into non-deterministic finite automata

The aim of the paper is to concoct a novel algorithm for the metamorphosis of parallel regular expressions to e-free non- deterministic finite automata. For a given parallel regular expression r, let m be the number of symbols that occur in r and let C denote the number of concatenation operators in r. In the worst case, 2 m+1 states are required for the construction of the non-deterministic finite automaton using the novel algorithm. In the earlier existing approaches, th e number of states of the non-deterministic finite automaton in the worst case is equal to 2 2jrj−3C.

The sandpile scheduler

This paper studies a self-organized criticality model called sandpile for dynamically load-balancing tasks arriving in the form of Bag-of-Tasks in large-scale decentralized system. The sandpile is designed as a decentralized agent system characterizing a cellular automaton, which works in a critical state at the edge of chaos. Depending on the state of the cellular automaton, different responses may occur when a new task is assigned to a resource: it may change nothing or generate avalanches that reconfigure the state of the system. The abundance of such avalanches is in power-law relation with their sizes, a scale-invariant behavior that emerges without requiring tuning or control parameters. That means that large—catastrophic—avalanches are very rare but small ones occur very often. Such emergent pattern can be efficiently adapted for non-clairvoyant scheduling, where tasks are load balanced in computing resources trying to maximize the performance but without assuming any knowledge on the tasks features. The algorithm design is experimentally validated showing that the sandpile is able to find near-optimal schedules by reacting differently to different conditions of workloads and architectures.

A Formal Model of Trust Chain based on Multi-level Security Policy

Trust chain is the core technology of trusted computing. A formal model of trust chain based on finite state automata theory is proposed. We use communicating sequential processes to describe the system state transition in trust chain and by combining with multi-level security strategy give the definition of trust system and trust decision theorem of trust chain transfer which is proved meantime. Finally, a prototype system is given to show the efficiency of the model. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3192

(t, n) threshold secret sharing scheme for nonlinear one-time pad

To address the problem that secret sharing scheme constructed by linear algorithm has security vulnerabilities,and to solve the problem that it easily leads to a single point of failure and unreliable situations with trusted party, this paper proposed a nonlinear threshold secret sharing scheme which combined nonlinear algorithm and cryptography. The scheme was based on two nonlinear structures of chaos algorithm and finite state automata, so it can generate random and dynamic shares.Participants can control each round shares to achieve the security level of once or N times a password. Secret was recovered by the Lagrange interpolation formula. Secure multiparty computation restricted every participant so that the scheme satisfied resilient equilibrium and could withstand chicanery or conspiracy attack.

HYPER-MINIMIZATION FOR DETERMINISTIC TREE AUTOMATA

Hyper-minimization is a recent automaton compression technique that can reduce the size of an automaton beyond the limits imposed by classical minimization. The additional compression power is enabled by allowing a finite difference in the represented language. The necessary theory for hyper-minimization is developed for (bottom-up) deterministic tree automata. The hyper-minimization problem for deterministic tree automata is reduced to the hyper-minimization problem for deterministic finite-state string automata, for which fast algorithms exist. The fastest algorithm obtained in this way runs in time [Formula: see text], where m is the size of the transition table and n is the number of states of the input tree automaton.

Fault Feature Extraction of High-Speed Automaton Based on Motion Morphology Decomposition

In order to obtain the characteristic parameters reflecting fault state of high-speed automaton (HSA), the fault feature extraction method based on motion morphology decomposition and wavelet packet transform (WPT) was presented. According to the movement law of the automaton, the vibration signal generated in three bursts of fire was decomposed into three separate signals, then the response signal in each shooting is a separate signal. Then using WPT to respectively extract wavelet packet energy from three separate signals as the fault characteristic parameters of HSA. By the example, the results show that the extracted fault features can well reflect the working conditions of automaton. Thus the proposed method could be used to extract the fault feature of automaton for monitoring the condition and diagnosing the fault of automaton.

Profile Trees for Büchi Word Automata, with Application to Determinization

The determinization of Buchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra, Piterman, Schewe, and others. Despite the proliferation of solutions, they are all essentially ad-hoc constructions, with little theory behind them other than proofs of correctness. Since Safra, all optimal constructions employ trees as states of the deterministic automaton, and transitions between states are defined operationally over these trees. The operational nature of these constructions complicates understanding, implementing, and reasoning about them, and should be contrasted with complementation, where a solid theory in terms of automata run DAGs underlies modern constructions. In 2010, we described a profile-based approach to Buchi complementation, where a profile is simply the history of visits to accepting states. We developed a structural theory of profiles and used it to describe a complementation construction that is deterministic in the limit. Here we extend the theory of profiles to prove that every run DAG contains a profile tree with at most a finite number of infinite branches. We then show that this property provides a theoretical grounding for a new determinization construction where macrostates are doubly preordered sets of states. In contrast to extant determinization constructions, transitions in the new construction are described declaratively rather than operationally.

Formal Verification Strategy for Statechart based Design of Reconfigurable Control of High Integrity Reactive Systems

Automated high integrity reactive systems required in the control of defence, automotive, rapid mass transport, manufacturing and healthcare systems, among many others, accentuate the need for formal specification and design tools. Reconfigurability by design is an added requirement given the costly development processes. Many of these systems are hybrids of discrete event and continuous-time subsystems. Statecharts (implemented as stateflow in Matlab) are increasingly being proposed as the language of choice for the discrete-event part. However, the complex semantics of statecharts make automated formal verification difficult and hence largely an unresolved problem. Formal verification, in preference to simulation/testing, is necessary to specify these systems at the required level of integrity and to maintain traceability along the different phases of design and operation. Drawing from a number of different approaches by others to develop formal semantics at requirement and implementation levels, a first attempt was made by the author to develop a modular formal verification strategy applicable to statechart based controller specifications for complex reactive systems and an early version of the original approach, which was completely based on regular languages (hence, finite state automata) and different compositions thereof, was published in 2005.The key idea was the implementation of these composition operations through suitably interpreted port structures between pairs of automata resulting from a decomposition of the statechart. Application development based on this model has been done with collaborators on an elevator test rig built for the purpose and still continuing. While many of the under lying concepts are still valid and there is much to be learnt from their practical implementation and extension, there are fundamental limitations in this model stemming from the rather basic computational and expressive power of regular languages. In the current paper the author attempts to extend the method to context­ free language based models (hence, pushdown automata, PDA) to include real-time semantics for internal (fast) events and general correctness properties expressed in temporal logic, posed as supervisory specifications of Ramage-Wonham type interpreted on the port structures between pairs of PDA whenever possible. It is shown that decidability problems limit this choice to restricted forms of context-free languages, and the development is done with Event-dock Visibly Pushdown Automata (ECVPA), which are dosed under Boolean operations and determinisable. The ECVPA based verification model is presented with high-speed railway signalling as a target environment.

Determinization of ordinal automata

It is proved that for each nondeterministic ordinal automaton there exists a deterministic ordinal automaton which is equivalent to the original one for all countable ordinals. An upper bound for the number of states of the deterministic automaton is double exponential in the number of states of the nondeterministic automaton.

Security policies enforcement using finite and pushdown edit automata

Edit automata have been introduced by J.Ligatti et al. as a model for security enforcement mechanisms which work at run time. In a distributed interacting system, they play a role of a monitor that runs in parallel with a target program and transforms its execution sequence into a sequence that obeys the security property. In this paper, we characterize security properties which are enforceable by finite edit automata (i.e. edit automata with a finite set of states) and deterministic context-free edit automata (i.e. finite edit automata extended with a stack). We prove that the properties enforceable by finite edit automata are a sub-class of regular sets. Moreover, given a regular set $$P$$ , one can decide in time $$O(n^2)$$ , whether $$P$$ is enforceable by a finite edit automaton (where $$n$$ is the number of states of the finite automaton recognizing $$P$$ ) and we give an algorithm to synthesize the controller. Moreover, we prove that safety policies are always enforced by a deterministic context-free edit automaton. We also prove that it is possible to check if a policy is a safety policy in $$O(n^4)$$ . Finally, we give a topological condition on the deterministic automaton expressing a regular policy enforceable by a deterministic context-free edit automaton.

Hilbert space formulation of symbolic systems for signal representation and analysis

Probabilistic finite state automata (PFSA) have been widely used as an analysis tool for signal representation and modeling of physical systems. This paper presents a new method to address these issues by bringing in the notion of vector-space formulation of symbolic systems in the setting of PFSA. In this context, a link is established between the formal language theory and functional analysis by defining an inner product space over a class of stochastic regular languages, represented by PFSA models that are constructed from finite-length symbol sequences. The norm induced by the inner product is interpreted as a measure of the information contained in the respective PFSA. Numerical examples are presented to illustrate the computational steps in the proposed method and to demonstrate model order reduction via orthogonal projection from a general Hilbert space of PFSA onto a (closed) Markov subspace that belongs to a class of shifts of finite type. These concepts are validated by analyzing time series of ultrasonic signals, collected from an experimental apparatus, for fatigue damage detection in polycrystalline alloys.

Duality Between a Deterministic Cellular Automaton and a Bosonic Quantum Field Theory in 1+1 Dimensions

Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue that quantum field theories may be much closer related to deterministic automata than what is usually thought possible.

Extracting ordinal temporal trail clusters in networks using symbolic time-series analysis

Temporal trails generated by agents traveling to various locations at different time epochs are becoming more prevalent in large social networks. We propose an algorithm to intuitively cluster groups of such agent trails from networks. The proposed algorithm is based on modeling each trail as a probabilistic finite state automata (PFSA). The algorithm also allows the specification of the required degree of similarity between the trails by specifying the depth of the PFSA. Hierarchical agglomerative clustering is used to group trails based on their representative PFSA and the locations that they visit. The algorithm was applied to simulated trails and real-world network trails obtained from merchant marine ships GPS locations. In both cases it was able to intuitively detect and extract the underlying patterns in the trails and form clusters of similar trails.

On One-to-One Dependence of Rebound Parameters on Statistics of Clusters: Exponential and Inverse-Power Distributions Out of Random Domino Automaton

The stochastic cellular automaton — a slowly driven system with avalanches — is proposed and an explicit one-to-one dependence between rebound parameters and statistics of clusters is investigated. Depending on the choice of the parameters determining the rule of the automaton, the model covers a wide range of properties: various types of exponential and long-tail (up to inverse-power) distributions of avalanches are observed. The stationary state of automaton is described by a set of nonlinear discrete equations derived from elementary combinatorial arguments. Formulas for average size of clusters and avalanches as well as for moments of arbitrary order are presented. Application of the automaton as a toy model of earthquakes and forest fires is presented. Utility as a test model for Ito equation is also pointed out.