The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce automata with delay blocks (ADBs), extending finite state automata with variable time delay blocks, for deferring individual transition output symbols, in a discrete-time setting. We show that the ADB languages strictly subsume the regular languages, and are incomparable in expressive power to the context-free languages. We show that ADBs are closed under union, concatenation and Kleene star, and under intersection with regular languages, but not closed under complementation and intersection with other ADB languages. We show that the emptiness and the membership problems are decidable in polynomial time for ADBs, whereas the universality problem is undecidable. Finally we consider the linear-time model checking problem, i.e., whether the language of an ADB is contained in a regular language, and show that the model checking problem is PSPACE-complete. Copyright 2012 ACM.
roceedings of the tenth ACM international conference on Embedded software
This work has been financially supported in part by the European Commission FP7-ICT Cognitive Systems, Interaction, and Robotics under the contract # 270180 (NOPTILUS); by Fundacao para Ciencia e Tecnologia under project PTDC/EEA-CRO/104901/2008 (Modeling and control of Networked vehicle systems in persistent autonomous operations); by Austrian Science Fund (FWF) Grant No P 23499-N23 on Modern Graph Algorithmic Techniques in Formal Verification; FWF NFN Grant No S11407-N23 (RiSE); ERC Start grant (279307: Graph Games); Microsoft faculty fellows award; ERC Advanced grant QUAREM; and FWF Grant No S11403-N23 (RiSE).
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EMSOFT: Embedded Software
2012-10-07 – 2012-10-12
Chatterjee K, Henzinger TA, Prabhu V. Finite automata with time delay blocks. In: Roceedings of the Tenth ACM International Conference on Embedded Software. ACM; 2012:43-52. doi:10.1145/2380356.2380370
Chatterjee, K., Henzinger, T. A., & Prabhu, V. (2012). Finite automata with time delay blocks. In roceedings of the tenth ACM international conference on Embedded software (pp. 43–52). Tampere, Finland: ACM. https://doi.org/10.1145/2380356.2380370
Chatterjee, Krishnendu, Thomas A Henzinger, and Vinayak Prabhu. “Finite Automata with Time Delay Blocks.” In Roceedings of the Tenth ACM International Conference on Embedded Software, 43–52. ACM, 2012. https://doi.org/10.1145/2380356.2380370.
K. Chatterjee, T. A. Henzinger, and V. Prabhu, “Finite automata with time delay blocks,” in roceedings of the tenth ACM international conference on Embedded software, Tampere, Finland, 2012, pp. 43–52.
Chatterjee K, Henzinger TA, Prabhu V. 2012. Finite automata with time delay blocks. roceedings of the tenth ACM international conference on Embedded software. EMSOFT: Embedded Software 43–52.
Chatterjee, Krishnendu, et al. “Finite Automata with Time Delay Blocks.” Roceedings of the Tenth ACM International Conference on Embedded Software, ACM, 2012, pp. 43–52, doi:10.1145/2380356.2380370.
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