Automata In Order Research Articles

Two dimensional fuzzy context-free languages and tiling patterns

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns.

Supervisory control of business processes with resources, parallel and mutually exclusive branches, loops, and uncertainty

A recent direction in Business Process Management studied methodologies to control the execution of Business Processes under several sources of uncertainty in order to always get to the end by satisfying all constraints. Current approaches encode business processes into temporal constraint networks or timed game automata in order to exploit their related strategy synthesis algorithms. However, the proposed encodings can only synthesize single-strategies and fail to handle loops. To overcome these limits we propose an approach based on supervisory control. We consider structured business processes with resources, parallel and mutually exclusive branches, loops, and uncertainty. We provide an encoding into finite state automata and prove that their concurrent behavior models exactly all possible executions of the process. After that, we introduce tentative commitment constraints as a new class of constraints restricting the executions of a process. We define a tree decomposition of the process that plays a central role in modular supervisory control, and we prove that this modular approach is equivalent to the monolithic one. We provide an algorithm to compute the finest tree decomposition to reduce the computational effort of synthesizing supervisors.

A conceptual flood model based on cellular automata for probabilistic risk applications.

This paper describes a simplified flood model based on cellular automata in order to be implemented in applications, which require the simulation of a great number of flood scenarios at regional scale. The model is based on a top-down evaluation of the flow process through the cells of the DEM. According to the conditions in a Moore Neighbourhood, the cells are classified in a dynamic process in four possible states with its own rules. To verify the quality of the results, an evaluation is carried out using the benchmarking tests and results shown in Neelz and Pender (2013). Besides, the 2D models HEC-RAS and Iber were used to evaluate quantitatively the efficiency of the model in terms of water depth and flood extent. From this, it is observed that the model produces very acceptable results especially where dynamic effects are less significant.

Dynamic Automaton-Guided Reward Shaping for Monte Carlo Tree Search

Reinforcement learning and planning have been revolutionized in recent years, due in part to the mass adoption of deep convolutional neural networks and the resurgence of powerful methods to refine decision-making policies. However, the problem of sparse reward signals and their representation remains pervasive in many domains. While various rewardshaping mechanisms and imitation learning approaches have been proposed to mitigate this problem, the use of humanaided artificial rewards introduces human error, sub-optimal behavior, and a greater propensity for reward hacking. In this paper, we mitigate this by representing objectives as automata in order to define novel reward shaping functions over this structured representation. In doing so, we address the sparse rewards problem within a novel implementation of Monte Carlo Tree Search (MCTS) by proposing a reward shaping function which is updated dynamically to capture statistics on the utility of each automaton transition as it pertains to satisfying the goal of the agent. We further demonstrate that such automaton-guided reward shaping can be utilized to facilitate transfer learning between different environments when the objective is the same.

Assessing complexity in cellular automata using information theory

ABSTRACTWe discuss two ways in which information theory can be used to assess complexity in a system of interacting agents. In the first part, we adopt a global viewpoint and propose a characterization of complexity based on successive maximum entropy estimations of the probability density describing the system, thereby quantifying the respective role played by low and high orders of interaction. In the second part we reconsider the question from a local perspective, focussing on the statistical dependencies between neighbouring agents. These tools are tried on simple cellular automata in order to put them in perspective with other notions of complexity usually employed for such systems. We show that these approaches are hardly comparable, despite some overlap in simple cases. However this allows to interpret complexity in terms of interactions at work in a system (instead of making reference to any particular realization of this dynamics), and to shed some light on the role of initial conditions in complex systems.Clustering of the 88 non-equivalent Elementary Cellular Automata according to their position in the space of information processing features. Rules are coloured according to their Wolfram class. ECA in class I are shown in black, class II in red, chaotic automata (class III) in green and automata displaying complex behaviour (class IV) in blue. In spite of some important important differences, information features and Wolfram class are seen to overlap to a certain extent.

The role of the interaction network in the emergence of diversity of behavior.

How can systems in which individuals’ inner workings are very similar to each other, as neural networks or ant colonies, produce so many qualitatively different behaviors, giving rise to roles and specialization? In this work, we bring new perspectives to this question by focusing on the underlying network that defines how individuals in these systems interact. We applied a genetic algorithm to optimize rules and connections of cellular automata in order to solve the density classification task, a classical problem used to study emergent behaviors in decentralized computational systems. The networks used were all generated by the introduction of shortcuts in an originally regular topology, following the small-world model. Even though all cells follow the exact same rules, we observed the existence of different classes of cells’ behaviors in the best cellular automata found—most cells were responsible for memory and others for integration of information. Through the analysis of structural measures and patterns of connections (motifs) in successful cellular automata, we observed that the distribution of shortcuts between distant regions and the speed in which a cell can gather information from different parts of the system seem to be the main factors for the specialization we observed, demonstrating how heterogeneity in a network can create heterogeneity of behavior.

Decision Problems on Unary Probabilistic and Quantum Automata

It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems. We also introduce the concept of linear recurrence automata in order to show the connection naturally. Then, we also give possible generalizations of linear recurrence relations and automata on vectors.

Early nested word automata for XPath query answering on XML streams

Algorithms for answering XPath queries on Xml streams have been studied intensively in the last decade. Nevertheless, there still exists no solution with high efficiency and large coverage. In this paper, we introduce early nested word automata in order to approximate earliest query answering algorithms for nested word automata. Our early query answering algorithm is based on stack-and-state sharing for running early nested word automata on all answer candidates with on-the-fly determinization. We prove tight upper complexity bounds on time and space consumption. We have implemented our algorithm in the QuiXPath system and show that it outperforms all previous tools in coverage on the XPathMark benchmark, while obtaining very high time and space efficiency and scaling to huge Xml streams. Furthermore, it turns out that our early query answering algorithm is earliest in practice on most queries from the XPathMark benchmark.11Thanks to the QuiXProc project of Inria and Innovimax and the CnrsSosp project.

A Hybrid Control Model to Develop the Trajectory-Tracking Controller for a Quadrotor UAV

A new hybrid model of control implementation is developed to realize trajectory-tracking controllers for quadrotor Unmanned Aerial Vehicles (UAV). This model is based on the Computational Fluid Dynamics (CFD) model and hybrid automata in order to accurately implement control parts of these vehicles, and can be applied to most standard quadrotor UAV platforms. The paper brings out step-by-step the controller development lifecycle for a quadrotor UAV, including the configuration and aerodynamic calculation model for the gathering preliminary inputs of the control application, the control analysis of dynamic model and general architecture, as well as the control design performed by specializing hybrid automata. The detailed design model is then converted into the implementation model by using open-source platforms in order to quickly simulate and realize the trajectory-tracking controller for this quadrotor UAV. Finally, this application was completely deployed and successfully taken on trial flights.

Modeling and verification of hybrid dynamic systems using multisingular hybrid Petri nets

The aim of this research has been to associate the modeling capacities of hybrid Petri nets with the analysis power of hybrid automata in order to perform formal verification of hybrid dynamic systems. In this paper, we propose an extension of hybrid Petri nets, called multisingular hybrid Petri nets (MSHPNs), for modeling and verification of hybrid dynamic systems. This extension consists of enriching hybrid Petri nets with the capabilities of hybrid automata to control the execution and firing of transitions and some modeling facilities for describing some repeatedly encountered aspects of timed and hybrid systems. We discuss the challenging issues of speed computation raised by addition of execution predicates and introduce a speed-based partitioning technique, which is essential for state space computation. We also introduce a method for reachability analysis of MSHPNs, consisting of computing the state class graph. Thus, the verification of timing properties of MSHPNs can be conducted using the existing techniques and tools. The proposed formalism has the expressiveness of multisingular hybrid automata besides the capabilities of Petri nets for modeling concurrent and distributed systems. Some illustrative examples of the proposed formalism are also presented in this paper.

Formal verification of components assembly based on SysML and interface automata

We propose an approach which combines component SysML models and interface automata in order to assemble components and to verify formally their interoperability. So we propose to verify formally t...

Is land-use change a cause of loss of pedodiversity? The case of the Mazzarrone study area, Sicily

Anthropogenic soils created ex novo by land-use change in large scale farming are, from a pedogenetic point of view, catastrophic events that bring the soils to time zero and change the natural pattern of the soilscape, remarkably, in some cases. The quantitative aspects of pedodiversity of a soilscape in South-East Sicily, where some types of soils, in recent decades, have suffered a consistent reduction due to the transformations by large scale farming, are considered. The evolution of pedodiversity over a 53-year period (1955 to 2008) is examined using a dedicated statistical method and a space–time model based on Markov analysis and cellular automata in order to predict the evolution of the soilscape pattern in the next 42 years (i.e. until 2050). Soil subgroups, using the USDA Soil Taxonomy and a classification proposal, were considered and the following indices were used: richness; Shannon's diversity index; Simpson diversity index; modified Simpson's diversity index; Shannon's evenness index; Simpson's evenness index and modified Simpson's evenness index. These indices measured over time, show, quantitatively, a decrease in pedodiversity that highlights the effect of the human intervention in modifying the natural order of the soilscape.

Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases

There are several ways of controlling the propagation of a contagious disease. For instance, to reduce the spreading of an airborne infection, individuals can be encouraged to remain in their homes and/or to wear face masks outside their domiciles. However, when a limited amount of masks is available, who should use them: the susceptible subjects, the infective persons or both populations? Here we employ susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations and probabilistic cellular automata in order to investigate how the deletion of links in the random complex network representing the social contacts among individuals affects the dynamics of a contagious disease. The inspiration for this study comes from recent discussions about the impact of measures usually recommended by health public organizations for preventing the propagation of the swine influenza A (H1N1) virus. Our answer to this question can be valid for other eco-epidemiological systems.

Streaming tree automata

Streaming validation and querying of XML documents are often based on automata for tree-like structures. We propose a new notion of streaming tree automata in order to unify the two main approaches, which have not been linked so far: automata for nested words or equivalently visibly pushdown automata, and respectively pushdown forest automata.

AN ALTERNATIVE CONSTRUCTION IN SYMBOLIC REACHABILITY ANALYSIS OF SECOND ORDER PUSHDOWN SYSTEMS

Recently, it has been shown that for any higher order pushdown system [Formula: see text] and for any regular set [Formula: see text] of configurations, the set [Formula: see text], is regular. In this paper, we give an alternative proof of this result for second order automata. Our construction of automaton for recognizing [Formula: see text] is explicit. The termination of saturation procedure used is obvious. It gives EXPTIME bound on size of the automaton recognizing [Formula: see text] if there is no alternation present in [Formula: see text] and in the automaton recognizing [Formula: see text].

Spatial configurations in a periurban city. A cellular automata-based microeconomic model

This paper presents a microeconomic model of residential location that explores the emergence of a mixed belt where residents and farmers coexist beyond a city. The model is based on integrating urban economics with cellular automata in order to simulate equilibrium patterns in 2D and through time. Households commute to a CBD and enjoy neighbourhood externalities that are a function of both local residential density and farmland, or open space. They bid on the competitive land market and locate so as to maximize utility. Incremental population growth changes the neighbourhood and leads to rent adaptations. With appropriate parameter values a mixed belt may emerge between the urban and agricultural specialized areas. Settlements within this mixed area are more or less clustered or scattered depending on preferences and neighbourhood size.

Formalizing Real-Time Scheduling Using Priority-Based Supervisory Control of Discrete-Event Systems

In this note, we formalize real-time task scheduling by applying an extension of supervisory control theory (SCT) of discrete-event systems to real-time models. The set of all possible timed traces of the system is specified by a discrete timed automaton where each transition is associated with an event occurrence or the passage of one unit of time. We introduce priorities to SCT, and apply them to the setting of discrete timed automata in order to develop a formal and unified framework for task scheduling on a single CPU.

Modelling a Secure Agent with Team Automata

We use Team Automata in order to model a protocol by Cachin et al. for securing agents in a hostile environment. Our study focuses on privacy properties of the agents. We use the framework to prove a result from the work by Cachin et al. As a by-product, our analysis gives some initial insight on the limits of the protocol. From a different perspective, this study continues a line of research on the expressive power and modelling capabilities of Team Automata. To the best of our knowledge, this is the first attempt to use Team Automata for the analysis of privacy properties.

Experimental study of Elementary Cellular Automata dynamics using the density parameter

Classifying cellular automata in order to capture the notion of chaos algorithmically is a challenging problem than can be tackled in many ways.We here give a classification based on the computation of a macroscopic parameter, the $d$-spectrum, and show how our classifying scheme can be used to separate the chaotic ECA from the non-chaotic ones.

Unary Context-Free Grammars and Pushdown Automata, Descriptional Complexity and Auxiliary Space Lower Bounds

It is well known that a context-free language defined over a one-letter alphabet is regular. This implies that unary context-free grammars and unary pushdown automata can be transformed into equivalent finite automata. In this paper, we study these transformations from a descriptional complexity point of view. In particular, we give optimal upper bounds for the number of states of nondeterministic and deterministic finite automata equivalent to unary context-free grammars in Chomsky normal form. These bounds are functions of the number of variables of the given grammars. We also give upper bounds for the number of states of finite automata simulating unary pushdown automata. As a main consequence, we are able to prove a log log n lower bound for the workspace used by one-way auxiliary pushdown automata in order to accept nonregular unary languages. The notion of space we consider is the so-called weak space concept.