11,283 research outputs found
Zone-based verification of timed automata: extrapolations, simulations and what next?
Timed automata have been introduced by Rajeev Alur and David Dill in the
early 90's. In the last decades, timed automata have become the de facto model
for the verification of real-time systems. Algorithms for timed automata are
based on the traversal of their state-space using zones as a symbolic
representation. Since the state-space is infinite, termination relies on finite
abstractions that yield a finite representation of the reachable states.
The first solution to get finite abstractions was based on extrapolations of
zones, and has been implemented in the industry-strength tool Uppaal. A
different approach based on simulations between zones has emerged in the last
ten years, and has been implemented in the fully open source tool TChecker. The
simulation-based approach has led to new efficient algorithms for reachability
and liveness in timed automata, and has also been extended to richer models
like weighted timed automata, and timed automata with diagonal constraints and
updates.
In this article, we survey the extrapolation and simulation techniques, and
discuss some open challenges for the future.Comment: Invited contribution at FORMATS'2
Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking
This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications
Cellular Automata are Generic
Any algorithm (in the sense of Gurevich's abstract-state-machine
axiomatization of classical algorithms) operating over any arbitrary unordered
domain can be simulated by a dynamic cellular automaton, that is, by a
pattern-directed cellular automaton with unconstrained topology and with the
power to create new cells. The advantage is that the latter is closer to
physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192
An Automata-Theoretic Approach to the Verification of Distributed Algorithms
We introduce an automata-theoretic method for the verification of distributed
algorithms running on ring networks. In a distributed algorithm, an arbitrary
number of processes cooperate to achieve a common goal (e.g., elect a leader).
Processes have unique identifiers (pids) from an infinite, totally ordered
domain. An algorithm proceeds in synchronous rounds, each round allowing a
process to perform a bounded sequence of actions such as send or receive a pid,
store it in some register, and compare register contents wrt. the associated
total order. An algorithm is supposed to be correct independently of the number
of processes. To specify correctness properties, we introduce a logic that can
reason about processes and pids. Referring to leader election, it may say that,
at the end of an execution, each process stores the maximum pid in some
dedicated register. Since the verification of distributed algorithms is
undecidable, we propose an underapproximation technique, which bounds the
number of rounds. This is an appealing approach, as the number of rounds needed
by a distributed algorithm to conclude is often exponentially smaller than the
number of processes. We provide an automata-theoretic solution, reducing model
checking to emptiness for alternating two-way automata on words. Overall, we
show that round-bounded verification of distributed algorithms over rings is
PSPACE-complete.Comment: 26 pages, 6 figure
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
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