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Presburger liveness verification of discrete timed automata

Zhe Dang, Pierluigi San Pietro, Richard A. Kemmerer
2003 Theoretical Computer Science  
We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds inÿnitely often for each !-path of A.  ...  Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on conÿgurations are allowed  ...  Section 2 introduces the main deÿnitions, such as discrete timed automata and the Presburger liveness properties.  ... 
doi:10.1016/s0304-3975(02)00485-1 fatcat:bzoe6gq3cne4zdhyszblu47iq4

Page 574 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
of discrete timed automata.  ...  We also show that other classes of Presburger liveness properties are indeed undecid- able for discrete timed automata, e.g., whether P holds infinitely often for each w-path of »/.  ... 

Liveness Verification of Reversal-Bounded Multicounter Machines with a Free Counter [chapter]

Zhe Dang, Oscar H. Ibarra, Pierluigi San Pietro
2001 Lecture Notes in Computer Science  
They can also be combined with [12] to study the same set of liveness problems on an extended form of discrete timed automata containing, besides clocks, a number of reversalbounded counters and a free  ...  We investigate the Presburger liveness problems for nondeterministic reversal-bounded multicounter machines with a free counter (NCMFs).  ...  The research presented in this paper is inspired by the recent work in [12] that investigates the same set of Presburger liveness problems for discrete timed automata.  ... 
doi:10.1007/3-540-45294-x_12 fatcat:kbopen22jjgatglczw6pr5myhq

The Existence of ω-Chains for Transitive Mixed Linear Relations and Its Applications [article]

Zhe Dang, Oscar Ibarra
2005 arXiv   pre-print
Using this result, we study a number of liveness verification problems for generalized timed automata within a unified framework.  ...  More precisely, we prove that (1) the mixed linear liveness problem for a timed automaton with dense clocks, reversal-bounded counters, and a free counter is decidable, and (2) the Presburger liveness  ...  Acknowledgements We would like to thank the following students at WSU for reading an earlier draft of this paper: K. Gjermundrod, H. He, A. Khodjanov, C. Li, J. Nelson, G. Xie, and L. Yang.  ... 
arXiv:cs/0110063v2 fatcat:tbvppjscrbaa5iibyyib4cftni

Author index

2003 Theoretical Computer Science  
Kemmerer, Presburger liveness verification of discrete timed automata (1-3) 413-438 Dang, Z., see O.H. Ibarra (1-3) 687-706 Das, S., see S.C. Nandy (1-3) 273-288 Durand, B., E. Formenti and Z. R !  ...  rank (1-3) 327-346 Fiorenzi, F., Cellular automata and strongly irreducible shifts of finite type (1-3) 477-493 Formenti, E., see B.  ... 
doi:10.1016/s0304-3975(03)00188-9 fatcat:homaqv6renfnrbiivkw6nrr3xy

Dense Counter Machines and Verification Problems [chapter]

Gaoyan Xie, Zhe Dang, Oscar H. Ibarra, Pierluigi San Pietro
2003 Lecture Notes in Computer Science  
There are applications of this result in verification, and we give one example in the paper.  ...  We also extend the notion of "semilinear language" to "dense semilinear language" and show its connection to a restricted class of dense multicounter automata.  ...  Ù Ø 4 Safety/Liveness Verification From the binary reachability characterizations given in the previous section, one can establish decidable results on various verification problems for a reversal-bounded  ... 
doi:10.1007/978-3-540-45069-6_8 fatcat:mfeo4n3ukrcypajx2cw7olpuai

Approaching Arithmetic Theories with Finite-State Automata [chapter]

Christoph Haase
2020 Lecture Notes in Computer Science  
The automata-theoretic approach provides an elegant method for deciding linear arithmetic theories.  ...  This approach has recently been instrumental for settling long-standing open problems about the complexity of deciding the existential fragments of Büchi arithmetic and linear arithmetic over p-adic fields  ...  It took, for instance, 50 years to show that Büchi's seminal approach for deciding Presburger arithmetic using finite-state automata runs in triply-exponential time and thus matches the upper bound of  ... 
doi:10.1007/978-3-030-40608-0_3 fatcat:y4yvocbpvzdcba4jlsttgv2nwq

Pushdown timed automata: a binary reachability characterization and safety verification

Zhe Dang
2003 Theoretical Computer Science  
The results are also extended to other generalizations of timed automata.  ...  We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a state, dense clock values and a stack word.  ...  A future research issue is to investigate whether the decidable results [22] for Presburger liveness of discrete timed automata can be extended to timed automata (with dense clocks) using the technique  ... 
doi:10.1016/s0304-3975(02)00743-0 fatcat:b7yjrvzgibhdlmjd5tmjzpy26u

The Effects of Bounding Syntactic Resources on Presburger LTL

Stephane Demri, Regis Gascon
2007 14th International Symposium on Temporal Representation and Reasoning (TIME'07)  
By way of example, we show that model-checking formulae from LTL with quantifier-free Presburger arithmetic over one-counter automata is only PSPACE-complete.  ...  Even the restriction to one counter has found applications in the verification of cryptographic protocols [21] and the validation of XML streams [9] .  ...  As additional corollaries, we deduce that the one-variable fragment of the counter logic L p [10] has a PSPACE-complete satisfiability problem and model-checking one-clock discrete timed automata with  ... 
doi:10.1109/time.2007.63 dblp:conf/time/DemriG07 fatcat:t5ezrbvzxvdvjmdkt2waoxeyx4

The Effects of Bounding Syntactic Resources on Presburger LTL

S. Demri, R. Gascon
2009 Journal of Logic and Computation  
By way of example, we show that model-checking formulae from LTL with quantifier-free Presburger arithmetic over one-counter automata is only PSPACE-complete.  ...  Even the restriction to one counter has found applications in the verification of cryptographic protocols [21] and the validation of XML streams [9] .  ...  As additional corollaries, we deduce that the one-variable fragment of the counter logic L p [10] has a PSPACE-complete satisfiability problem and model-checking one-clock discrete timed automata with  ... 
doi:10.1093/logcom/exp037 fatcat:cvjzyvtqurfitjyst3egbl6tma

Formal verification of timed systems: a survey and perspective

Farn Wang
2004 Proceedings of the IEEE  
An overview of the current state of the art of formal verification of real-time systems is presented.  ...  We also make a few comments according to our experience with verification tool design and implementation.  ...  Bisimulation-based verification of timed automata can be found in [71] , [153] . Work on discrete-time models can be found in [147] - [149] . D.  ... 
doi:10.1109/jproc.2004.831197 fatcat:7e5u5rvdbncqbmkku7szkdyz34

Page 8490 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Kem- merer, On Presburger liveness of discrete timed automata (132- 143); Frangois Denis, Aurélien Lemay and Alain Terlutte, Resid- ual finite state automata (144-157); Anders Dessmark and An- drzej Pelc  ...  construction of a universal extended H system (226-239); Chuzo Iwamoto, Kat- suyuki Tateishi, Kenichi Morita and Katsunobu Imai, Speeding-up cellular automata by alternations (240-251); Martin Kutrib,  ... 

Algorithmic Metatheorems for Decidable LTL Model Checking over Infinite Systems [chapter]

Anthony Widjaja To, Leonid Libkin
2010 Lecture Notes in Computer Science  
of infinite-state systems including pushdown systems; prefix-recognizable systems; reversal-bounded counter systems with discrete clocks and a free counter; concurrent pushdown systems with a bounded  ...  class of infinite systems, but over a large family of classes of infinite systems.  ...  Discrete timed counter systems (RCM and d-RCM). Although verifying safety and liveness for general counter machines is undecidable, it is known that these problems are decidable (cf.  ... 
doi:10.1007/978-3-642-12032-9_16 fatcat:qeltq5zo3ndyjkhceyksple6se

Algorithmic metatheorems for decidable LTL model checking over infinite systems [article]

Anthony Widjaja To, Leonid Libkin
2009 arXiv   pre-print
of infinite-state systems including pushdown systems; prefix-recognizable systems; reversal-bounded counter systems with discrete clocks and a free counter; concurrent pushdown systems with a bounded  ...  class of infinite systems, but over a large family of classes of infinite systems.  ...  Discrete timed counter systems (RCM and d-RCM). Although verifying safety and liveness for general counter machines is undecidable, it is known that these problems are decidable (cf.  ... 
arXiv:0910.4932v2 fatcat:zpg4jzxyk5cwxabhjd7ubxipnq

Embedded and Real-time Systems [chapter]

Edward L. Lamie
2009 Real-Time Embedded Multithreading Using ThreadX  
Verification models and techniques applied to testing and control of reactive systems RESEARCH CENTER Rennes -Bretagne-Atlantique THEME Embedded and Real Time Systems Project-Team VERTECS  ...  , and verification of communicating timed automata.  ...  In the context of verification, we also use Timed Automata.  ... 
doi:10.1016/b978-1-85617-601-9.00001-2 fatcat:oo46lkp3gnbhbjc463pu7fs2hi
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