This paper presents algorithms for the automatic synthesis of real-time controllers by finding a winning strategy for certain games defined by the timed-automata of Alur and Dill. In such games, the outcome depends on the players' actions as well as on their timing. We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications.

On the synthesis of discrete controllers for timed systems

In this chapter we give an introduction to active learning of Mealy machines, an automata model particularly suited for modeling the behavior of realistic reactive systems. Active learning is characterized by its alternation of an exploration phase and a testing phase. During exploration phases so-called membership queries are used to construct hypothesis models of a system under learning. In testing phases so-called equivalence queries are used to compare respective hypothesis models to the actual system. These two phases are iterated until a valid model of the target system is produced.

/pdf/introduction-to-active-automata-learning-from-a-practical-me3nlieal8.pdf

Introduction to Active Automata Learning from a Practical Perspective

Checking language inclusion between two nondeterministic Buchi automata A and B is computationally hard (PSPACE-complete). However, several approaches which are efficient in many practical cases have been proposed. We build on one of these, which is known as the Ramsey-based approach. It has recently been shown that the basic Ramsey-based approach can be drastically optimized by using powerful subsumption techniques, which allow one to prune the search-space when looking for counterexamples to inclusion. While previous works only used subsumption based on set inclusion or forward simulation on A and B, we propose the following new techniques: (1) A larger subsumption relation based on a combination of backward and forward simulations on A and B. (2) A method to additionally use forward simulation between A and B. (3) Abstraction techniques that can speed up the computation and lead to early detection of counterexamples. The new algorithm was implemented and tested on automata derived from real-world model checking benchmarks, and on the Tabakov-Vardi random model, thus showing the usefulness of the proposed techniques.

/pdf/advanced-ramsey-based-buchi-automata-inclusion-testing-23g5c934l2.pdf

Advanced Ramsey-based Büchi automata inclusion testing

This book constitutes the refereed proceedings of the 19th International Conference on Concurrency Theory, CONCUR 2008, held in Toronto, Canada, August 19-22, 2008. The 33 revised full papers presented together with 2 tool papers were carefully reviewed and selected from 120 submissions. The topics include model checking, process calculi, minimization and equivalence checking, types, semantics, probability, bisimulation and simulation, real time, and formal languages.

CONCUR 2008 - Concurrency Theory: 19th International Conference, CONCUR 2008, Toronto, Canada, August 19-22, 2008, Proceedings

Symbolic Automata extend classical automata by using symbolic alphabets instead of finite ones. Most of the classical automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In this paper we study the problem of minimizing symbolic automata. We formally define and prove the basic properties of minimality in the symbolic setting, and lift classical minimization algorithms (Huffman-Moore's and Hopcroft's algorithms) to symbolic automata. While Hopcroft's algorithm is the fastest known algorithm for DFA minimization, we show how, in the presence of symbolic alphabets, it can incur an exponential blowup. To address this issue, we introduce a new algorithm that fully benefits from the symbolic representation of the alphabet and does not suffer from the exponential blowup. We provide comprehensive performance evaluation of all the algorithms over large benchmarks and against existing state-of-the-art implementations. The experiments show how the new symbolic algorithm is faster than previous implementations.

/pdf/minimization-of-symbolic-automata-2pq5uwr248.pdf

Minimization of symbolic automata

We present an efficient algorithm to reduce the size of nondeterministic Buchi word automata, while retaining their language. Additionally, we describe methods to solve PSPACE-complete automata problems like universality, equivalence and inclusion for much larger instances (1-3 orders of magnitude) than before. This can be used to scale up applications of automata in formal verification tools and decision procedures for logical theories.The algorithm is based on new transition pruning techniques. These use criteria based on combinations of backward and forward trace inclusions. Since these relations are themselves PSPACE-complete, we describe methods to compute good approximations of them in polynomial time.Extensive experiments show that the average-case complexity of our algorithm scales quadratically. The size reduction of the automata depends very much on the class of instances, but our algorithm consistently outperforms all previous techniques by a wide margin. We tested our algorithm on Buchi automata derived from LTL-formulae, many classes of random automata and automata derived from mutual exclusion protocols, and compared its performance to the well-known automata tool GOAL.

/pdf/advanced-automata-minimization-1fzm5u7ren.pdf

Advanced automata minimization

There are two main classes of methods for checking universality and language inclusion of Buchi-automata: Rank-based methods and Ramsey-based methods While rank-based methods have a better worst-case complexity, Ramsey-based methods have been shown to be quite competitive in practice [10,9] It was shown in [10] (for universality checking) that a simple subsumption technique, which avoids exploration of certain cases, greatly improves the performance of the Ramsey-based method Here, we present a much more general subsumption technique for the Ramsey-based method, which is based on using simulation preorder on the states of the Buchi-automata This technique applies to both universality and inclusion checking, yielding a substantial performance gain over the previous simple subsumption approach of [10].

/pdf/simulation-subsumption-in-ramsey-based-buchi-automata-2zlm5gffvb.pdf

Simulation subsumption in ramsey-based büchi automata universality and inclusion testing

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.

https://hal.inria.fr/hal-01373546/document

Non-Zero Sum Games for Reactive Synthesis

We present an efficient algorithm to reduce the size of nondeterministic Buchi word automata, while retaining their language. Additionally, we describe methods to solve PSPACE-complete automata problems like universality, equivalence and inclusion for much larger instances (1-3 orders of magnitude) than before. This can be used to scale up applications of automata in formal verification tools and decision procedures for logical theories. The algorithm is based on new transition pruning techniques. These use criteria based on combinations of backward and forward trace inclusions. Since these relations are themselves PSPACE-complete, we describe methods to compute good approximations of them in polynomial time. Extensive experiments show that the average-case complexity of our algorithm scales quadratically. The size reduction of the automata depends very much on the class of instances, but our algorithm consistently outperforms all previous techniques by a wide margin. We tested our algorithm on Buchi automata derived from LTL-formulae, many classes of random automata and automata derived from mutual exclusion protocols, and compared its performance to the well-known automata tool GOAL.

Lorenzo Clemente

Papers

Advanced Ramsey-based Büchi automata inclusion testing

Advanced automata minimization

Simulation subsumption in ramsey-based büchi automata universality and inclusion testing

Non-Zero Sum Games for Reactive Synthesis

Advanced Automata Minimization