Model matching for finite-state machines

The problem of model matching for finite state machines (FSMs) consists of finding a controller for a given open-loop system so that the resulting closed-loop system matches a desired input-output behavior. In this paper, a set of model matching problems is addressed: strong model matching (where the reference model and the plant are deterministic FSMs and the initial conditions are fixed), strong model matching with measurable disturbances (where disturbances are present in the plant), and strong model matching with nondeterministic reference model (where any behavior out of those in the reference model has to be matched by the closed-loop system). Necessary and sufficient conditions for the existence of controllers for all these problems are given. A characterization of all feasible control laws is derived and an efficient synthesis procedure is proposed. Further, the well-known supervisory control problem for discrete-event dynamical systems (DEDSs) formulated in its basic form is shown to be solvable as a strong model matching problem with measurable disturbances and nondeterministic reference model     

A music notation construction engine for optical music recognition

Optical music recognition (OMR) systems are used to convert music scanned from paper into a format suitable for playing or editing on a computer. These systems generally have two phases: recognizing the graphical symbols (such as note‐heads and lines) and determining the musical meaning and relationships of the symbols (such as the pitch and rhythm of the notes). In this paper we explore the second phase and give a two‐step approach that admits an economical representation of the parsing rules for the system. The approach is flexible and allows the system to be extended to new notations with little effort—the current system can parse common music notation, Sacred Harp notation and plainsong. It is based on a string grammar and a customizable graph that specifies relationships between musical objects. We observe that this graph can be related to printing as well as recognizing music notation, bringing the opportunity for cross‐fertilization between the two areas of research. Copyright © 2003 John Wiley & Sons, Ltd.     

Model reduction of finite-state machines by contraction

This paper discusses an approach to the model reduction of discrete event systems represented by finite-state machines. A set of good reduced-order approximations of a deterministic finite-state machine M can be efficiently computed by looking at its contractions, i.e., finite-state machines constructed from M by merging two states. In some particular case, it is also possible to prove that the approximations thus constructed are infimal, in the sense that there do not exist better approximations with the same number of states. This paper also defines a merit function to choose, among a set of approximations, the best one with respect to a given observed behavior     

Implementation of supervisory control using extended finite-state machines

This article aims at bridging the gap between traditional designs to discrete-event control problems and supervisory control theory of Ramadge and Wonham. We propose to implement supervisory control by extending the plant's finite state machine with Boolean variables, guard formulas and updating functions. Boolean variables are used to encode the supervisor's states, event observation is captured by a set of Boolean functions that update the value of variables, and control is introduced by guarding events with Boolean formulas. The framework developed in this work is fundamental in our ongoing research on communication between supervisors in a distributed discrete-event system.     

On a class of optimal abstractions of finite-state machines

Anabstraction A of an fsmM consists in partitioning its states, inputs, and outputs into groups, thus turning it into a non-deterministic fsmM _A. For fixed sets of states, inputs, and outputs, and abstraction generally maps a number of machinesM defined on these sets into the sameM _A. We would like to find anoptimal abstractionA ^* which minimizes this number, while lumping the states, inputs, and outputs into a specified number of classes. We extend these ideas to an fsmM operating in a random environment, and show that the abstraction results in a probabilistic fsm . Thinking of changes inM's output map as resulting in machinesM≠MM, we want to find anA ^* that minimizes the number ofMM which are such that the transition probabilities of their abstracted version are identical to those of the specification machine . SuchMM arise from statistically-undetectable output faults inM. Abstractions are directly applicable to the monitoring of a complex system by an observer for deviations from correct behavior (faults). Complex systems are usually accessible through restricted interfaces, which do not allow the observer to distinguish among all states, inputs, and outputs, thus rendering some faulty transitions undetectable. An optimal interface design will minimize the number of such undetectable faults. Assuming that only single-transition output faults occur inM, we show that each of the classes into which the abstraction lumps the outputs contributes a number of undetectable output faults. We then show that the problem of partitioning the outputs into a given number of classes that minimizes the maximum of these numbers is NP-complete. However, we give (a) an approximate minimization algorithm, running in time linear in the number of classes and quadratic in the number ofM's outputs, and (b) a lower bound on the minimum, computable in the same amount of time. The concept of optimal abstractions is illustrated by numerical results on combinational logic circuits that perform arithmetical operations. The results shed light on the trade-off between model simplification and the ability to detect erroneous behaviors in complex systems.     

Minimization of mealy finite-state machines by internal states gluing

A problem of minimization of Mealy finite-state machines that is common in synthesizing digital devices on programmable logic devices is considered. The proposed approach uses an operation of gluing two states and represents the finite-state machine as a list of transitions. Cases when gluing two states generates wait states are described. Algorithms that minimize the number of internal states, the number of transitions and input variables of Mealy finite-state machines are given. The experimental results showed that when used to implement finite-state machines on programmable logic devices, the proposed method helps decrease the implementation cost 1.31 times on average and 3 times at best. Topical directions for further study of finite-state machines minimization methods are given.     

Unboundedness detection for a class of communicating finite-state machines

Let M and N be two communicating finite-state machines that exchange one type of message. We discuss an algorithm to decide whether the communication between M and N is bounded. The algorithm is based on constructing a finite representation of the reachability tree of M and N assuming that M and N progress at equal speeds.     

Complexity of ideals in finite semigroups and finite-state machines

# _G (S) denotes the complexity of a finite semigroup as introduced by Krohn and Rhodes. IfI is a maximal ideal or maximal left ideal of a semigroupS, then# _G (I) ? # _G (S) ? # _G (I) + 1. Thus, ifV is an ideal ofS with# _G (S) = n ? k = # _G (V), then there is a chain of ideals ofS

$$V = V_k \subset V_{k + 1} \subset ... \subset V_n \subseteq S$$     

Computational capabilities of local-feedback recurrent networksacting as finite-state machines

In this paper we explore the expressive power of recurrent networks with local feedback connections for symbolic data streams. We rely on the analysis of the maximal set of strings that can be shattered by the concept class associated to these networks (i.e. strings that can be arbitrarily classified as positive or negative), and find that their expressive power is inherently limited, since there are sets of strings that cannot be shattered, regardless of the number of hidden units. Although the analysis holds for networks with hard threshold units, we claim that the incremental computational capabilities gained when using sigmoidal units are severely paid in terms of robustness of the corresponding representation.     

A framework for compositional nonblocking verification of extended finite-state machines

This paper presents a framework for compositional nonblocking verification of discrete event systems modelled as extended finite-state machines (EFSM). Previous results are improved to consider general conflict-equivalence based abstractions of EFSMs communicating both via shared variables and events. Performance issues resulting from the conversion of EFSM systems to finite-state machine systems are avoided by operating directly on EFSMs, deferring the unfolding of variables into state machines as long as possible. Several additional methods to abstract EFSMs and remove events are also presented. The proposed algorithm has been implemented in the discrete event systems tool Supremica, and the paper presents experimental results for several large EFSM models that can be verified faster than by previously used methods.     

Stable encoding of finite-state machines in discrete-time recurrent neural nets with sigmoid units

There has been a lot of interest in the use of discrete-time recurrent neural nets (DTRNN) to learn finite-state tasks, with interesting results regarding the induction of simple finite-state machines from input-output strings. Parallel work has studied the computational power of DTRNN in connection with finite-state computation. This article describes a simple strategy to devise stable encodings of finite-state machines in computationally capable discrete-time recurrent neural architectures with sigmoid units and gives a detailed presentation on how this strategy may be applied to encode a general class of finite-state machines in a variety of commonly used first- and second-order recurrent neural networks. Unlike previous work that either imposed some restrictions to state values or used a detailed analysis based on fixed-point attractors, our approach applies to any positive, bounded, strictly growing, continuous activation function and uses simple bounding criteria based on a study of the conditions under which a proposed encoding scheme guarantees that the DTRNN is actually behaving as a finite-state machine.     

Nonconcurrent error detection and correction in fault-tolerant linear finite-state machines

In this paper, we construct fault-tolerant linear finite-state machines (LFSMs) in which error detection and correction can be performed nonconcurrently (e.g., periodically). More specifically, by jointly choosing the state encoding constraints and the redundant dynamics of the fault-tolerant LFSM, we enable an external checker to detect and identify errors due to past faults based on the current, possibly corrupted state of the LFSM. The paper presents systematic constructions of fault-tolerant LFSMs based on a characterization of nonconcurrent error detection/correction in terms of state encoding constraints and redundant dynamics. In particular, we develop a scheme that uses Bose-Chaudhuri-Hocquenghem (BCH) coding and obtains fault-tolerant LFSMs that require 2D additional state variables and have the ability to correct up to D errors in any state variable at any time step in the time interval consisting of the latest N time steps of operation. The construction uses the minimum possible number of additional state variables and requires an error detecting/correcting mechanism with computational complexity that is only linear in N.     

Video editing with pen-based technology

Multimedia Tools and Applications - The manipulation of video content is still a difficult task due to its complexity and richness. This paper applies pen-based technology to video editing, with...     

A graph grammar programming style for recognition of music notation

Graph grammars are a promising tool for solving picture processing problems. However, the application of graph grammars to diagram recognition has been limited to rather simple analysis of local symbol configurations. This paper introduces the Build-Weed-Incorporate programming style for graph grammars and shows its application in determining the meaning of complex diagrams, where the interaction among physically distant symbols is semantically important. Diagram recognition can be divided into two stages: symbol recognition and high-level recognition. Symbol recognition has been studied extensively in the literature. In this work we assume the existence of a symbol recognizer and use a graph grammar to assemble the diagram's information content from the symbols and their spatial relationships. The Build-Weed-Incorporate approach is demonstrated by a detailed discussion of a graph grammar for high-level recognition of music notation. See Appendix A for an illustration of the terms for musical symbols used in this paper.     

Minimization of incompletely specified mealy finite-state machines by merging two internal states

A heuristic method for the minimization of Mealy finite state machines (FSMs) with unspecified values of the output variables based on merging two states is considered. Necessary and sufficient conditions for the possibility to merge two states and for forming wait states are given. Algorithms for determining the set of state pairs that can be merged, algorithms for finding the best pair for merging, and for the minimization of the number of FSM states and FSM input variables are presented. The proposed method makes it possible to reduce the number of internal states by a factor of 1.22 on the average and sometimes even by a factor of 2.75. The number of FSM transitions is reduced by a factor of 1.32 on the average and sometimes by a factor of 2.27. Compared with the well-known STAMINA computer program, the proposed method does not reduce the number of states but considerably reduces the number of transitions by a factor of 1.55 on the average and sometimes by a factor of 3.92.     

A method for minimizing Moore finite-state machines by merging two states

The problem of minimization of Moore finite-state machines (FSMs) is considered. This problem often arises in designing digital devices based on programmable logic devices. The proposed approach uses the operation of merging of two states of an FSM and the representation of the FSM as a list of transitions. Conditions guaranteeing the identical operation and deterministic behavior of the transformed FSM obtained by merging two states are given. The cases when wait states can emerge are also discussed. Algorithms for minimizing the number of internal states, transition paths, and the number input variables of Moore FSMs are described. Experimental results have shown that the proposed approach reduces the number of internal states by 6% on the average and sometimes by a factor of 1.86; the number of transitions is reduced by 20% on the average and sometimes by a factor of 2.83. The use of the proposed method in combination with the STAMINA computer program reduces the number of internal states by 16% on the average and sometimes by a factor of 2.17; the number of transitions is reduced by 41% on the average and sometimes by a factor of 7.97. In conclusion, important directions of research concerning the minimization of FSMs are discussed.     

Optimal transfer trees and distinguishing trees for testing observable nondeterministic finite-state machines

The fault-state detection approach for blackbox testing consists of two phases. The first is to bring the system under test (SUT) from its initial state to a targeted state t and the second is to check various specified properties of the SUT at t. This paper investigates the first phase for testing systems specified as observable nondeterministic finite-state machines with probabilistic and weighted transitions. This phase involves two steps. The first step transfers the SUT to some state t' and the second step identifies whether t' is indeed the targeted state t or not. State transfer is achieved by moving the SUT along one of the paths of a transfer tree (TT) and state identification is realized by using diagnosis trees (DT). A theoretical foundation for the existence and characterization of TT and DT with minimum weighted height or minimum average weight is presented. Algorithms for their computation are proposed.