Verifying and comparing finite state machines for systems that have distributed interfaces

This paper concerns state-based systems that interact with their environment at physically distributed interfaces, called ports. When such a system is used a projection of the global trace, a local trace, is observed at each port. As a result the environment has reduced observational power: the set of local traces observed need not define the global trace that occurred. We consider the previously defined implementation relation ⊆s and prove that it is undecidable whether N ⊆s M and so it is also undecidable whether testing can distinguishing two states or FSMs. We also prove that a form of model-checking is undecidable when we have distributed observations and give conditions under which N ⊆s M is decidable. We then consider implementation relation ⊆sk that concerns input sequences of length κ or less. If we place bounds on κ and the number of ports then we can decide N ⊆sk M in polynomial time but otherwise this problem is NP-hard

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing

Analysing the Efficiency of Algorithms for Compiling Finite-State Morphologies

Äärellistilaiset morfologiat ovat tietokoneohjelmia, jotka mallintavat kielen sanojen rakennetta (morfologiaa) merkkijonopareja sisältävillä tietorakenteilla (äärellistilaisilla transduktoreilla). Äärellistilaisia morfologioita voidaan käyttää esimerkiksi hakuohjelmissa, jotka löytävät tekstistä kaikki annetun perusmuotoisen sanan esiintymät eri taivutusmuodoissaan. Äärellistilaiset morfologiat ovat myös hyödyllisiä, kun tekstistä tehdään tilastoja siitä kuinka usein kukin sana esiintyy ja missä taivutusmuodoissa. Äärellistilaisten morfologioiden rakentaminen on monimutkainen prosessi, johon kuuluu useita tehtäviä, joista yksi on transduktorin minimointi. Yleisiä minimointialgoritmeja ovat Brzozowskin (BRZ) ja Hopcroftin algoritmit (HOP). Kirjallisuudessa esiintyy väitteitä, joiden mukaan BRZ:n ja HOP:n välinen ero on merkityksettömän pieni morfologioita käännettäessä. Kuitenkaan BRZ:n suorituskykyä ei ole järjestelmällisesti testattu tai verrattu HOP:iin missään tutkimuksessa. Tässä diplomityössä käännettiin HFST-ohjelmistolla kaksi avoimen lähdekoodin morfologiaa, suomelle kirjoitettu OMorFi ja saksalle kirjoitettu Morphisto. HFST perustuu kahteen avoimen lähdekoodin transduktoriohjelmistopakettiin, SFST:hen ja OpenFst:hen, joista edellinen käyttää BRZ:ia ja jälkimmäinen HOP:ia minimointialgoritmina. BRZ osoittautui paljon hitaammaksi kuin HOP sekä suomen että saksan morfologioilla. BRZ:n hitaus oli ilmeistä transduktoreissa, jotka sisälsivät suuren mittakaavan syklisyyttä eli niissä oli siirtymiä, jotka johtivat lopputilojen läheisyydestä alkutilan läheisyyteen. Tällaisia transduktoreita esiintyy usein morfologioissa, joissa on yhdyssanamekanismi. Jos HOP:n ja BRZ:n välillä on valittava, edellinen on parempi vaihtoehto minimointi-algoritmiksi. BRZ on joskus nopeampi kuin HOP, mutta siinä tapauksessa algoritmien ero on melko pieni. Niissä tapauksissa joissa BRZ on hitaampi kuin HOP, ero on huomattavasti suurempi: BRZ on joskus jopa 50 kertaa hitaampi kuin HOP. BRZ on kuitenkin paljon helpompi toteuttaa, koska se perustuu kahteen perusoperaatioon, determinisointiin ja reversioon. Jos HOP:n toteuttaminen on liian vaativa tehtävä, avoimen lähdekoodin transduktorikirjaston kehittäjät voivat käyttää OpenFst:n minimointialgoritmia. Transduktorit voidaan muuntaa OpenFst:n muotoon, minimoida OpenFst:llä ja muuntaa takaisin alkuperäiseen muotoon. Tätä ratkaisua on tarkoitus käyttää myös HFST:n tulevissa versioissa.Finite-state morphologies (FSMs) are computer programs that model the structure of words in a language (morphology) with networks containing a number of string pairs (finite-state transducers). FSMs can be used e.g. to implement search programs that can find all forms of a word in a document if they are given only the base form. FSMs are also useful in compiling statistics on a text, i.e. finding out how often a word occurs and in which forms. Constructing FSMs is a complex process involving many tasks, one of which is transducer minimisation. Common minimisation algorithms include Brzozowski's (BRZ) and Hopcroft's algorithm (HOP). There have been claims in the literature that often the difference between BRZ and HOP is insignificant when compiling FSMs. However, no studies have been carried out where the performance of BRZ would have been systematically tested or compared with HOP. In this thesis, we compiled two open-source morphologies, OMorFi for Finnish and Morphisto for German, with the HFST software. HFST is based on two open-source transducer software packages, SFST and OpenFst, the former using BRZ and the latter HOP as a minimisation algorithm. BRZ turned out to be much slower than HOP both on Finnish and German morphologies. The slowness of BRZ was evident in transducers that contained large-scale cyclicity, i.e. had transitions leading from the nearness of the final states to the nearness of initial states. These kinds of transducers often occur in morphologies that have a compounding mechanism. If a choice must be made between HOP and BRZ, the previous is a better choice for a minimisation algorithm. BRZ is sometimes faster than HOP, but in that case their difference is quite small. In the cases where BRZ is slower than HOP, their difference is much bigger, BRZ sometimes being 50 times slower than HOP. Of course, BRZ is much easier to implement since it uses two basic operations, determinisation and reversion. If the implementation of HOP is considered too demanding a task, the developers of free-source transducer libraries can use OpenFst's minimisation algorithm. The transducers can be converted to OpenFst format, minimised with OpenFst and converted back to the original format. This solution will also be used in future versions of HFST

Modular Decomposition of Hierarchical Finite State Machines

In this paper we develop an analogue of the graph-theoretic `modular decomposition' in automata theory. This decomposition allows us to identify hierarchical finite state machines (HFSMs) equivalent to a given finite state machine (FSM). We provide a definition of a module in an FSM, which is a collection of nodes which can be treated as a nested FSM. We identify a well-behaved subset of FSM modules called thin modules, and represent these using a linear-space directed graph we call a decomposition tree. We prove that every FSM has a unique decomposition tree which uniquely stores each thin module. We provide an $O(n^2k)$ algorithm for finding the decomposition tree of an $n$-state $k$-alphabet FSM. The decomposition tree allows us to extend FSMs to equivalent HFSMs. For thin HFSMs, which are those where each nested FSM is a thin module, we can construct an equivalent maximally-hierarchical HFSM in polynomial time.Comment: 38 pages, 11 figures. Submitted to Theoretical Computer Scienc

Discovering Models of Software Processes from Event-Based Data ; CU-CS-819-96

Many software process methods and tools presuppose the existence of a formal model of a process. Unfortunately, developing a formal model for an on-going, complex process can be dicult, costly, and error prone. This presents a practical barrier to the adoption of process technologies, which would be lowered by automated assistance in creating formal models. To this end, we have developed a data analysis technique that we term process discovery. Under this technique, data describing process events are rst captured from an on-going process and then used to generate a formal model of the behavior of that process. In this paper we describe a Markov method that we developed specically for process discovery, as well as describe two additional methods that we adopted from other domains and augmented for our purposes. The three methods range from the purely algorithmic to the purely statistical. We compare the methods and discuss their application in an industrial case study

Counter-constrained finite state machines: modelling component protocols with resource-dependencies

This report deals with the specification of software component protocols (i.e., the set of service call sequences). The contribution of this report is twofold: (a) We discuss specific requirements of real-world protocols, especially in the presence of components wich make use of limited resources. (b) We define counter-constrained finite state machines (CC-FSMs), a novel extension of finite state machines, specifically created to model protocols having dependencies between services due to their access to shared resources. We provide a theoretical framework for reasoning and analysing CC-FSMs. Opposed to finite state machines and other approaches, CC-FSMs combine two valuable properties: (a) CC-FSMs are powerful enough to model realistic component protocols with resource allocation, usage, and de-allocation dependencies between methods (as occurring in common abstract datatypes such as stacks or queues) and (b) CC-FSMs have a decidabile equivalence- and inclusion problem as proved in this report by providing algorithms for efficient checking equivalence and inclusion. These algorithms directly lead to efficient checks for component interoperability and substitutability. Keywords: software component protocols, finite state machine extension, decidable inclusion check, interoperability, substitutability

Specific-to-General Learning for Temporal Events with Application to Learning Event Definitions from Video

We develop, analyze, and evaluate a novel, supervised, specific-to-general learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, event-description language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positive-examples--only specific-to-general learning method based on these algorithms. We also present a polynomial-time--computable ``syntactic'' subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally, we apply this algorithm to the task of learning relational event definitions from video and show that it yields definitions that are competitive with hand-coded ones