On determinism versus nondeterminism for restarting automata

AbstractA restarting automaton processes a given word by executing a sequence of local simplifications until a simple word is obtained that the automaton then accepts. Such a computation is expressed as a sequence of cycles. A nondeterministic restarting automaton M is called correctness preserving, if, for each cycle u⊢Mcv, the string v belongs to the characteristic language LC(M) of M, if the string u does. Our first result states that for each type of restarting automaton X∈{R,RW,RWW,RL,RLW,RLWW}, if M is a nondeterministic X-automaton that is correctness preserving, then there exists a deterministic X-automaton M1 such that the characteristic languages LC(M1) and LC(M) coincide. When a restarting automaton M executes a cycle that transforms a string from the language LC(M) into a string not belonging to LC(M), then this can be interpreted as an error of M. By counting the number of cycles it may take M to detect this error, we obtain a measure for the influence that errors have on computations. Accordingly, this measure is called error detection distance. It turns out, however, that an X-automaton with bounded error detection distance is equivalent to a correctness preserving X-automaton, and therewith to a deterministic X-automaton. This means that nondeterminism increases the expressive power of X-automata only in combination with an unbounded error detection distance

26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

Choice and chance:model-based testing of stochastic behaviour

Probability plays an important role in many computer applications. A vast number of algorithms, protocols and computation methods uses randomisation to achieve their goals. A crucial question then becomes whether such probabilistic systems work as intended. To investigate this, such systems are often subjected to a large number of well-designed test cases, that compare a observed behaviour to a requirements specification. Model-based testing is an innovative testing technique rooted in formal methods, that aims at automating this labour intense and often error-prone manual task. By providing faster and more thorough testing at lower cost, it has gained rapid popularity in industry and academia alike. However, classic model-based testing methods are insufficient when dealing with inherently stochastic systems. This thesis introduces a rigorous model-based testing framework, that is capable to automatically test such systems. The presented methods are capable of judging functional correctness, discrete probability choices, and hard and soft-real time constraints. The framework is constructed in a clear step-by-step approach. First, the model-based testing landscape is laid out, and related work is discussed. Next, we instantiate a model-based testing framework to highlight the purpose of individual theoretical components like, e.g., a conformance relation, test cases, and practical test generation algorithms. This framework is then conservatively extended by introducing discrete probability choices to the specification language. A last step further extends this probabilistic framework by adding hard and soft real time constraints. Classical functional correctness verdicts are thus extended with goodness of fit methods known from statistics. Proofs of the framework’s correctness are presented before its capabilities are exemplified by studying smaller scale case studies known from the literature. The framework reconciles non-deterministic and probabilistic choices in a fully-fledged way via the use of schedulers. Schedulers then become a subject worthy to study in their own rights. This is done in the second part of this thesis; we introduce a most natural equivalence relation based on schedulers for Markov automata, and compare its distinguishing power to notions of trace distributions and bisimulation relations. Lastly, the power of different scheduler classes of stochastic automata is investigated. We compare reachability probabilities of different schedulers by altering the information available to them. A hierarchy of scheduler classes is established, with the intent to reduce complexity of related problems by gaining near optimal results for smaller scheduler classes

Alternative Automata-based Approaches to Probabilistic Model Checking

In this thesis we focus on new methods for probabilistic model checking (PMC) with linear temporal logic (LTL). The standard approach translates an LTL formula into a deterministic ω-automaton with a double-exponential blow up. There are approaches for Markov chain analysis against LTL with exponential runtime, which motivates the search for non-deterministic automata with restricted forms of non-determinism that make them suitable for PMC. For MDPs, the approach via deterministic automata matches the double-exponential lower bound, but a practical application might benefit from approaches via non-deterministic automata. We first investigate good-for-games (GFG) automata. In GFG automata one can resolve the non-determinism for a finite prefix without knowing the infinite suffix and still obtain an accepting run for an accepted word. We explain that GFG automata are well-suited for MDP analysis on a theoretic level, but our experiments show that GFG automata cannot compete with deterministic automata. We have also researched another form of pseudo-determinism, namely unambiguity, where for every accepted word there is exactly one accepting run. We present a polynomial-time approach for PMC of Markov chains against specifications given by an unambiguous Büchi automaton (UBA). Its two key elements are the identification whether the induced probability is positive, and if so, the identification of a state set inducing probability 1. Additionally, we examine the new symbolic Muller acceptance described in the Hanoi Omega Automata Format, which we call Emerson-Lei acceptance. It is a positive Boolean formula over unconditional fairness constraints. We present a construction of small deterministic automata using Emerson-Lei acceptance. Deciding, whether an MDP has a positive maximal probability to satisfy an Emerson-Lei acceptance, is NP-complete. This fact has triggered a DPLL-based algorithm for deciding positiveness

Preparation and control of intelligent automation systems

In the automation systems of tomorrow, it is likely that the devices included have various degrees of autonomy, and include advanced algorithms for perception and control. Human operators will be expected to work together with collaborative robots as well as with roaming robots for material handling.The volatile nature of the environment of such intelligent automation systems lead to an enormous amount of possible situations that can arise and which need to be suitably handled. This complexity makes development of control systems for intelligent automation systems difficult using traditional methods.As an alternative, this thesis presents a model-based control framework, which uses a combination of formal specification and automated planning. The proposed framework allows for defining the intentions of the automation system on a high level, which enables decisions that influence when things should occur to be modeled using logical constraints, rather than programming. To achieve a modular framework, low level, reusable, resource models are composed by 1) formal specification to ensure safety and 2) applying an abstraction called an operation, which couples the reusable resources to the intentions of the system. By planning also the resources\u27 detailed actions, the operations can, when possible, be completed regardless of the resources\u27 current state. This eases error-recovery, as resources do not have to be reset when an error occurs.Additionally, the thesis proposes an iterative and interactive workflow for integrating the proposed model-based control framework into a virtual preparation process, using computer-based simulation as a tool for validating formal specifications. The control framework allows for adding new constraints to a running system, enabling an efficient and interactive preparation process.The framework has been applied to a use case from final assembly, which features human-robot collaboration. Experimental results on the ability to handle unforeseen errors and planning performance are presented

Safe Programming Over Distributed Streams

The sheer scale of today\u27s data processing needs has led to a new paradigm of software systems centered around requirements for high-throughput, distributed, low-latency computation.Despite their widespread adoption, existing solutions have yet to provide a programming model with safe semantics -- and they disagree on basic design choices, in particular with their approach to parallelism. As a result, naive programmers are easily led to introduce correctness and performance bugs. This work proposes a reliable programming model for modern distributed stream processing, founded in a type system for partially ordered data streams. On top of the core type system, we propose language abstractions for working with streams -- mechanisms to build stream operators with (1) type-safe compositionality, (2) deterministic distribution, (3) run-time testing, and (4) static performance bounds. Our thesis is that viewing streams as partially ordered conveniently exposes parallelism without compromising safety or determinism. The ideas contained in this work are implemented in a series of open source software projects, including the Flumina, DiffStream, and Data Transducers libraries