56 research outputs found
When is Containment Decidable for Probabilistic Automata?
The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous
Reasoning about Regular Properties: A Comparative Study
Several new algorithms for deciding emptiness of Boolean combinations of
regular languages and of languages of alternating automata (AFA) have been
proposed recently, especially in the context of analysing regular expressions
and in string constraint solving. The new algorithms demonstrated a significant
potential, but they have never been systematically compared, neither among each
other nor with the state-of-the art implementations of existing
(non)deterministic automata-based methods. In this paper, we provide the first
such comparison as well as an overview of the existing algorithms and their
implementations. We collect a diverse benchmark mostly originating in or
related to practical problems from string constraint solving, analysing LTL
properties, and regular model checking, and evaluate collected implementations
on it. The results reveal the best tools and hint on what the best algorithms
and implementation techniques are. Roughly, although some advanced algorithms
are fast, such as antichain algorithms and reductions to IC3/PDR, they are not
as overwhelmingly dominant as sometimes presented and there is no clear winner.
The simplest NFA-based technology may be actually the best choice, depending on
the problem source and implementation style. Our findings should be highly
relevant for development of these techniques as well as for related fields such
as string constraint solving
Project Final Report Use and Dissemination of Foreground
This document is the final report on use and dissemination of foreground, part of the CONNECT final report. The document provides the lists of: publications, dissemination activities, and exploitable foregroun
Approximate automata for omega-regular languages
Automata over infinite words, also known as ω -automata, play a key role in the verification and synthesis of reactive systems. The spectrum of ω -automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic ω -automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism.
In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition
Parameterized Synthesis with Safety Properties
Parameterized synthesis offers a solution to the problem of constructing
correct and verified controllers for parameterized systems. Such systems occur
naturally in practice (e.g., in the form of distributed protocols where the
amount of processes is often unknown at design time and the protocol must work
regardless of the number of processes). In this paper, we present a novel
learning based approach to the synthesis of reactive controllers for
parameterized systems from safety specifications. We use the framework of
regular model checking to model the synthesis problem as an infinite-duration
two-player game and show how one can utilize Angluin's well-known L* algorithm
to learn correct-by-design controllers. This approach results in a synthesis
procedure that is conceptually simpler than existing synthesis methods with a
completeness guarantee, whenever a winning strategy can be expressed by a
regular set. We have implemented our algorithm in a tool called L*-PSynth and
have demonstrated its performance on a range of benchmarks, including robotic
motion planning and distributed protocols. Despite the simplicity of L*-PSynth
it competes well against (and in many cases even outperforms) the
state-of-the-art tools for synthesizing parameterized systems.Comment: 18 page
Three variations of observation equivalence preserving synthesis abstraction
In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor
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