Highly Undecidable Problems For Infinite Computations

We show that many classical decision problems about 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are $\Pi_2^1$-complete, hence located at the second level of the analytical hierarchy, and "highly undecidable". In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all $\Pi_2^1$-complete for context-free omega-languages or for infinitary rational relations. Topological and arithmetical properties of 1-counter omega-languages, context free omega-languages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1-counter automata or 2-tape automata.Comment: to appear in RAIRO-Theoretical Informatics and Application

A Model-Derivation Framework for Software Analysis

Model-based verification allows to express behavioral correctness conditions like the validity of execution states, boundaries of variables or timing at a high level of abstraction and affirm that they are satisfied by a software system. However, this requires expressive models which are difficult and cumbersome to create and maintain by hand. This paper presents a framework that automatically derives behavioral models from real-sized Java programs. Our framework builds on the EMF/ECore technology and provides a tool that creates an initial model from Java bytecode, as well as a series of transformations that simplify the model and eventually output a timed-automata model that can be processed by a model checker such as UPPAAL. The framework has the following properties: (1) consistency of models with software, (2) extensibility of the model derivation process, (3) scalability and (4) expressiveness of models. We report several case studies to validate how our framework satisfies these properties.Comment: In Proceedings MARS 2017, arXiv:1703.0581

A Model-Derivation Framework for Software Analysis

Model-based verification allows to express behavioral correctness conditions like the validity of execution states, boundaries of variables or timing at a high level of abstraction and affirm that they are satisfied by a software system. However, this requires expressive models which are difficult and cumbersome to create and maintain by hand. This paper presents a framework that automatically derives behavioral models from real-sized Java programs. Our framework builds on the EMF/ECore technology and provides a tool that creates an initial model from Java bytecode, as well as a series of transformations that simplify the model and eventually output a timed-automata model that can be processed by a model checker such as UPPAAL. The framework has the following properties: (1) consistency of models with software, (2) extensibility of the model derivation process, (3) scalability and (4) expressiveness of models. We report several case studies to validate how our framework satisfies these properties.Comment: In Proceedings MARS 2017, arXiv:1703.0581

Polychronous Interpretation of Synoptic, a Domain Specific Modeling Language for Embedded Flight-Software

The SPaCIFY project, which aims at bringing advances in MDE to the satellite flight software industry, advocates a top-down approach built on a domain-specific modeling language named Synoptic. In line with previous approaches to real-time modeling such as Statecharts and Simulink, Synoptic features hierarchical decomposition of application and control modules in synchronous block diagrams and state machines. Its semantics is described in the polychronous model of computation, which is that of the synchronous language Signal.Comment: Workshop on Formal Methods for Aerospace (FMA 2009

Timed Automata Semantics for Analyzing Creol

We give a real-time semantics for the concurrent, object-oriented modeling language Creol, by mapping Creol processes to a network of timed automata. We can use our semantics to verify real time properties of Creol objects, in particular to see whether processes can be scheduled correctly and meet their end-to-end deadlines. Real-time Creol can be useful for analyzing, for instance, abstract models of multi-core embedded systems. We show how analysis can be done in Uppaal.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499

時間プッシュダウンオートマトンの表現力と到達可能性問題

筑波大学 (University of Tsukuba)201

Modelamiento y especificación de sistemas distribuidos y temporizados

El aumento en la complejidad de los sistemas distribuidos y temporizados hace que ellos sean muy difícil de modelary especificar correctamente. Diferentes métodos formales son útiles para el proceso de modelado y especificaciónde estos tipos de sistemas. Los Autómatas Temporizados (AT) y los Autómatas Temporizados Distribuidos (ATD)son los modelos formales más utilizados para modelar sistemas de tiempo real y distribuidos. Lamentablemente losalgoritmos existentes para calcular la inclusión y complementación de sus lenguajes son indecidible. En este artículo,presentaremos las lógicas (Lógica Temporalizada de Eventos Distribuidos, Lógica Temporizados de Memorizaciónde Eventos) y los autómatas (Autómatas de Eventos Distribuidos, Autómatas de Memorización de Eventos),totalmente decidibles. Estos métodos fueron diseñados para modelar, especificar, estudiar el comportamiento y enespecial verificar el buen funcionamiento de los sistemas de tiempo real y distribuidos.Increasing complexity in distributed and real-time systems makes them very hard to model and specify correctly. Different formal methods are useful for the process of modeling and specification of these kinds of systems. Timed Automata (TA) and Distributed Timed Automata (DTA) are the dominant models of distributed and realtime systems. Unfortunately, their language inclusion and complementation are undecidable. In this paper, we will present logics and automata (Distributed Event Clock Automata (DECA), Memory Event Clock Automata (RMECA), Distributed Event Clock Temporal Logic (DECTL), Memory Event Clock Temporal Logic (RMECTL) fully decidable and they were designed to modeling, specifying and studying the behavior and in particular verifying the correct operation of distributed and real-time systems

Synchronizing Data Words for Register Automata

Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data from an infinite domain. We study the concept of synchronizing data words in RAs: does there exist a data word that sends all states of the RA to a single state? For deterministic RAs with k registers (k-DRAs), we prove that inputting data words with 2k+1 distinct data from the infinite data domain is sufficient to synchronize. We show that the synchronization problem for DRAs is in general PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of the RA) might be necessary to synchronize. The synchronization problem for NRAs is in general undecidable, however, we establish Ackermann-completeness of the problem for 1-NRAs. Another main result is the NEXPTIME-completeness of the length-bounded synchronization problem for NRAs, where a bound on the length of the synchronizing data word, written in binary, is given. A variant of this last construction allows to prove that the length-bounded universality problem for NRAs is co-NEXPTIME-complete

Reductions and Abstractions for Optimization of Modular Timed Automata

Time optimization of concurrent sequences of operations is in this paper solved by timed automata. To reduce the complexity of this classical problem, including applications such as planning and scheduling, an abstraction method has recently been proposed based on local optimization (Hagebring and Lennartson, 2019). In a modular subsystem, local paths without any communication with other subsystems are optimized with respect to time, and when subsystems are synchronized more local behavior appears. The proposed method has shown to be successful, drastically reducing computational complexity for important classes of planning problems. The only drawback is that the synchronous composition includes a heuristic non-standard synchronous composition procedure to achieve true con currency. In this paper a simple solution to this problem is presented based on the original synchronous composition of timed automata. In the transformation of the timed automaton to an ordinary automaton, where time weights are generated, it is first observed that the state space often increases dramatically in this transformation. To solve this complexity problem, an efficient reduction is proposed as a complement to local optimization, and both methods are demonstrated to be very efficient when they are applied to realistic benchmark examples. Copyright (C) 2022 The Authors