Finite-state Process Research Articles

A generic framework for checking semantic equivalences between pushdown automata and finite-state automata

For a given process equivalence, we say that a process g is fully equivalent to a process f of a transition system T if g is equivalent to f and every reachable state of g is equivalent to some state of T. We propose a generic method for deciding full equivalence between pushdown processes and finite-state processes applicable to every process equivalence satisfying certain abstract conditions. Then, we show that these conditions are satisfied by bisimulation-like equivalences (including weak and branching bisimilarity), weak simulation equivalence, and weak trace equivalence, which are the main conceptual representatives of the linear/branching time spectrum. The list of particular results obtained by applying our method includes items which are first of their kind, and the associated upper complexity bounds are essentially optimal.

Realizability of concurrent recursive programs

We study the realizability problem for concurrent recursive programs: given a distributed system architecture and a sequential specification over words, find a distributed automata implementation that is equivalent to the specification. This problem is well-studied as far as finite-state processes are concerned, and it has a solution in terms of Zielonka’s Theorem. We lift Zielonka’s Theorem to the case where processes are recursive and modeled as visibly pushdown (or, equivalently, nested-word) automata. However, contrarily to the finite-state case, it is undecidable whether a specification is realizable or not. Therefore, we also consider suitable underapproximation techniques from the literature developed for multi-pushdown systems, and we show that they lead to a realizability framework with effective algorithms.

Finite state estimation and control of a multi-input CSTR benchmark

The problem of curse-of-dimensionality in finite state and action Markov decision processes is considered using iterative clustering of closed-loop data and repeated discretization of the state space process model. The performance of the control design approach is demonstrated using a multi-input van der Vusse continuous stirred tank reactor control benchmark. It is demonstrated that the finite state description provides a simple implementation of Bayesian state estimation using cell filters, and dynamic programming gives means to conduct optimization of closed-loop performance of a nonlinear stochastic multidimensional chemical plant.

Mean square detectability of LTI systems over finite-state digital block-fading channels

This paper studies the mean square quadratic (MSQ) detectability for multi-output networked systems over finite-state digital block-fading channels. The packet-loss rate of each digital fading channel depends on the channel power gain, as well as packet length and power level used for transmission. A finite-state random process is introduced to model time-varying fading channels, which characterizes various configurations of physical communication environment and/or different channel fading amplitudes. Necessary and sufficient conditions for MSQ detectability over finite-state Markov digital block-fading channels are given in the form of algebraic Riccati equations or linear matrix inequalities (LMIs). The estimation gain is given as a function of estimated/observed channel state. In addition, explicit conditions on network for MSQ detectability over finite-state independent identically distributed (i.i.d.) digital block-fading channels are presented in terms of the unstable poles of the multi-output plant. Finally, an application to Gilbert-Elliott channels (GECs) is provided to demonstrate the derived results.

Compiling, verifying and simulating dynamic software architectures using ANTLR and coloured-ADL

The concept of reconfigurable and dynamic software architecture (DSA) occupies today an important place in the field of software engineering. As result, several architecture description languages (ADLs) and approaches have been proposed for describing DSA in the highest level of abstraction. However, most of these works present theoretical solutions without giving an idea on the execution of final systems at run time. In this paper, we propose a new DSA called coloured software architecture (CSA) based on two concepts coloured operation and coloured connector. Then, we propose a new ADL called coloured-ADL and implement a compiling, verification and simulation tool dedicated to CSA. The simulation of system instances, derived from a CSA, is mainly used to explain coloured-ADL and evaluate the reliability of the simulated system. On the other hand, the verification is focused on checking a new defined safety property called architectural stack overflow (ASO). A safe CSA should be free of ASO violation property. To check a CSA, the verification uses also finite state processes (FSP) and labelled transition state (LTS) to expect this kind of property. We illustrate our propositions through two case studies from the literature.

Compiling, verifying and simulating dynamic software architectures using ANTLR and coloured-ADL

The concept of reconfigurable and dynamic software architecture (DSA) occupies today an important place in the field of software engineering. As result, several architecture description languages (ADLs) and approaches have been proposed for describing DSA in the highest level of abstraction. However, most of these works present theoretical solutions without giving an idea on the execution of final systems at run time. In this paper, we propose a new DSA called coloured software architecture (CSA) based on two concepts coloured operation and coloured connector. Then, we propose a new ADL called coloured-ADL and implement a compiling, verification and simulation tool dedicated to CSA. The simulation of system instances, derived from a CSA, is mainly used to explain coloured-ADL and evaluate the reliability of the simulated system. On the other hand, the verification is focused on checking a new defined safety property called architectural stack overflow (ASO). A safe CSA should be free of ASO violation property. To check a CSA, the verification uses also finite state processes (FSP) and labelled transition state (LTS) to expect this kind of property. We illustrate our propositions through two case studies from the literature.

Formal framework for distributed swarm computing: abstract model and properties

Swarm computing is an emerging computing paradigm suitable for solving difficult optimization problems by employing a nature-inspired search for solutions. A set of entities called swarm entities populates a digital space that emulates a real physical environment. The digital space acts as a container of swarm entities by providing the basic functionalities for the entities management including processing and migration. Swarm entities are modeled as computational objects that follow a specific set of behavioral laws of natural inspiration. The entities are organized as a swarm, i.e., they coordinate, collaborate and act by exchanging information either directly or indirectly via the environment, seeking to solve a difficult computational optimization problem. Our main research result reported in this paper is the proposal of a new formal computational model of a generic distributed framework for swarm computing. Our model captures the basic computational properties of the swarm using the formal language of Finite State Process algebra. The proposed model is simple, clear and abstract, i.e., technology independent. It can serve as a starting basis for further refinement and subsequent development of new concurrent and/or distributed implementations using the available distributed computing technologies.

Quantifying communication in synchronized languages

A mutual information rate is proposed to quantitatively evaluate inter-process synchronized communication. For finite-state processes with implicit communication that can be described by a counting language, it is shown that the mutual information rate is effectively computable. When the synchronization always happens between the same two symbols at the same time (or with a fixed delay), the mutual information rate is computable. In contrast, when the delay is not fixed, the rate is not computable. Finally, it is shown that some cases exist where the mutual information rate is not computable.

Simple and efficient local codes for distributed stable network construction

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction, we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol. Moreover, we assume pairwise interactions between the processes that are scheduled by a fair adversary. In order to allow processes to construct networks, we let them activate and deactivate their pairwise connections. When two processes interact, the protocol takes as input the states of the processes and the state of their connection and updates all of them. Initially all connections are inactive and the goal is for the processes, after interacting and activating/deactivating connections for a while, to end up with a desired stable network. We give protocols (optimal in some cases) and lower bounds for several basic network construction problems such as spanning line, spanning ring, spanning star, and regular network. The expected time to convergence of our protocols is analyzed under a uniform random scheduler. Finally, we prove several universality results by presenting generic protocols that are capable of simulating a Turing Machine (TM) and exploiting it in order to construct a large class of networks. We additionally show how to partition the population into ksupernodes, each being a line of $$\log k$$logk nodes, for the largest such k. This amount of local memory is sufficient for the supernodes to obtain unique names and exploit their names and their memory to realize nontrivial constructions.

Integrating behavior analysis into architectural modeling

Architectural modeling and behavior analysis are two important concerns in the software development. They are often implemented separately, and specified by their own supporting notations. Architectural modeling helps to guarantee the system design to satisfy the requirement, and behavior analysis can ensure the interaction correctness. To improve the trustworthiness, methods trying to combine architectural modeling and behavior analysis notations together have been proposed, e.g., establishing a one-way mapping relation. However, the one-way relation cannot ensure updating one notation specifications in accordance with the other one, which results in inconsistency problems. In this paper, we present an approach to integrating behavior analysis into architectural modeling, which establishes the interoperability between architectural modeling notation and behavior analysis notation by a bidirectional mapping. The architecture is specified by the modeling language, architecture analysis and design language (AADL), and then mapped to behavior analysis notation, Darwin/FSP (finite state process) through the bidirectional transformation. The bidirectional transformation provides traceability, which makes behavior analysis result provided by a model checker can be traced and reflected back to the original AADL specifications. In this way, the behavior analysis is integrated into architectural modeling. The feasibility of our approach is shown by a control system example.

Finite-TimeH∞Control for a Class of Discrete-Time Markov Jump Systems with Actuator Saturation via Dynamic Antiwindup Design

We deal with the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. The proposed conditions allow us to find dynamic anti-windup compensator which stabilize the closed-loop systems in the finite-time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.

Finite-TimeH∞Control for Discrete-Time Markov Jump Systems with Actuator Saturation

This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-timeH∞controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

An Algorithm for the Identification of Components in Biochemical Pathways

Biochemical pathways are abstract descriptions of the interactions among the molecular species involved in a process. Different molecular species mentioned in a pathway often represent different states of the same biological entity (e.g. the unbound and bound states of a certain molecule). Hence, a pathway can be seen as a network of interactions between entities which may change state synchronously by means of reactions. We consider such biological entities as pathway components and define a semi-automatic algorithm to infer the components from their interactions described in the pathway. Since this problem is inherently ambiguous, interaction with a domain expert might be needed to resolve any ambiguity that should arise. We apply the algorithm to the identification of components in a model of the EGF signaling pathway from the literature, and discuss possible uses of the component categorization as regards (i) the extraction of subpathways by projecting over a subset of components, and (ii) the automatic translation into finite state automata or process algebra terms.

Collective Phenomena and Non-Finite State Computation in a Human Social System

We investigate the computational structure of a paradigmatic example of distributed social interaction: that of the open-source Wikipedia community. We examine the statistical properties of its cooperative behavior, and perform model selection to determine whether this aspect of the system can be described by a finite-state process, or whether reference to an effectively unbounded resource allows for a more parsimonious description. We find strong evidence, in a majority of the most-edited pages, in favor of a collective-state model, where the probability of a “revert” action declines as the square root of the number of non-revert actions seen since the last revert. We provide evidence that the emergence of this social counter is driven by collective interaction effects, rather than properties of individual users.

A modified hidden Markov model

This paper considers two discrete time, finite state processes X and Y. In the usual hidden Markov model X modulates the values of Y. However, the values of Y are then i.i.d. given X. In this paper a new model is considered where the Markov chain X modulates the transition probabilities of the second, observed chain Y. This more realistically can represent problems arising in DNA sequencing. Algorithms for all related filters, smoothers and parameter estimations are derived. Versions of the Viterbi algorithms are obtained.

A generalized Girsanov transformation of finite state stochastic processes in discrete time

Cohen and Elliott (2010) introduced the backward stochastic difference equations (BSDEs) on spaces related to discrete time, finite state processes. Motivated by obtaining the explicit solution of a linear BSDE under their framework, we develop a new type of Girsanov transformation in this paper.

A quadratic construction for Zielonka automata with acyclic communication structure

Asynchronous automata are parallel compositions of finite-state processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be recognized by a deterministic asynchronous automaton. The construction is rather involved and the most efficient variant produces automata which are exponential in the number of processes and polynomial in the size of the DFA.In this paper we show a simple, quadratic construction in the case where the synchronization actions are binary and define an acyclic communication graph.

Software Model Checking SystemC

SystemC is an increasingly used language for writing executable specifications of systems-on-chip. The verification of SystemC, however, is a very difficult challenge. Simulation features great scalability, but can miss important defects. On the other hand, formal verification of SystemC is extremely hard because of the presence of threads, and the intricacies of the communication and scheduling mechanisms. In this paper, we explore formal verification for SystemC by means of software model checking techniques, which have demonstrated substantial progress in recent years. We propose an accurate model of SystemC and three complementary encodings of SystemC to finite-state processes, sequential and threaded programming models. We implement the proposed approaches in a tool chain and carry out a thorough experimental evaluation using several benchmarks taken from the literature on SystemC verification, and experimenting with different state-of-the-art software model checkers. The results clearly show the applicability and efficiency of the proposed approaches. In particular, the results show the effectiveness of the threaded and of the finite-model encodings to prove and disprove properties, respectively.

Bootstrap confidence bands for sojourn distributions in multistate semi-Markov models with right censoring

Transient semi-Markov processes have traditionally been used to describe the transitions of a patient through the various states of a multistate survival model. A survival distribution in this context is a sojourn through the states until passage to a fatal absorbing state or certain endpoint states. Using complete sojourn data, this paper shows how such survival distributions and associated hazard functions can be estimated nonparametrically and also how nonparametric bootstrap pointwise confidence bands can be constructed for them when patients are subject to independent right censoring from each state during the sojourn. Limitations to the estimability of such survival distributions that result from random censoring with bounded support are clarified. The methods are applicable to any sort of sojourn through any finite state process of arbitrary complexity involving feedback into previously occupied states.

Information theory, model error, and predictive skill of stochastic models for complex nonlinear systems

Many problems in complex dynamical systems involve metastable regimes despite nearly Gaussian statistics with underlying dynamics that is very different from the more familiar flows of molecular dynamics. There is significant theoretical and applied interest in developing systematic coarse-grained descriptions of the dynamics, as well as assessing their skill for both short- and long-range prediction. Clustering algorithms, combined with finite-state processes for the regime transitions, are a natural way to build such models objectively from data generated by either the true model or an imperfect model. The main theme of this paper is the development of new practical criteria to assess the predictability of regimes and the predictive skill of such coarse-grained approximations through empirical information theory in stationary and periodically-forced environments. These criteria are tested on instructive idealized stochastic models utilizing K-means clustering in conjunction with running-average smoothing of the training and initial data for forecasts. A perspective on these clustering algorithms is explored here with independent interest, where improvement in the information content of finite-state partitions of phase space is a natural outcome of low-pass filtering through running averages. In applications with time-periodic equilibrium statistics, recently developed finite-element, bounded-variation algorithms for nonstationary autoregressive models are shown to substantially improve predictive skill beyond standard autoregressive models.