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## Verification for Timed Automata extended with Unbounded Discrete Data Structures

### Citations

2640 | A Theory of Timed Automata
- Alur, Dill
- 1994
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Citation Context ... paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable. 1 Introduction Timed automata were introduced by Alur and Dill =-=[4]-=-, and have since then become a popular standard formalism to model real-time systems. An undeniable reason for the success of timed automata is the PSPACE decidability of the language emptiness proble... |

360 |
Ordering by divisibility in abstract algebras
- Higman
- 1952
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Citation Context ...1a2 . . . am ∗ a′1a ′ 2 . . . a ′ n if there exists a strictly increasing function f : {1, . . . ,m} → {1, . . . , n} such that for all i ∈ {1, . . . ,m} we have ai a′f(i). Lemma 4 (Higman’s Lemma =-=[22]-=-). 1. If and ⊑ are well-quasi-orders on A and B, respectively, then the product of and ⊑ is a well-quasi-order on (A×B). 2. If is a well-quasi-order on A, then the monotone domination order ∗ i... |

301 |
On communicating finite-state machines
- Brand, Zafiropulo
- 1983
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Citation Context ...there an error-free computation of C from (sI , ε) to (sF , x) for some x ∈M∗? The control state reachability problem is undecidable for channel machines, because channel machines are Turing-powerful =-=[12,2]-=-. The proof of Th. 1 is a reduction of the control state reachability problem for channel machines. The idea of the reduction is as follows: Given a channel machine C, we define a timed language L(C) ... |

188 | Visibly Pushdown Languages
- Alur, Madhusudan
- 2004
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Citation Context ...implies the decidability of the universality problem for one-counter nets. Further we know that the universality and language inclusion problems are decidable if A and B are visibly pushdown automata =-=[6]-=-. Hence it is interesting to consider the two problems for the corresponding subclasses of timed pushdown automata. It turns out that the decidability status changes depending from whether the model u... |

157 |
Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors
- Dickson
- 1913
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Citation Context ...3, . . . in A there exist indices i < j such that ai aj . A standard example for a well-quasi-order is the component-wise ordering ≤k on the set Nk of vectors of k natural numbers (Dickson’s Lemma, =-=[17]-=-). Let be a quasi-order on A, and let ⊑ be a quasi-order on B. We define the product of and ⊑ on (A × B) by (a, b) ≤ (a′, b′), if and only if, a a′ and b ⊑ b′. We define the monotone domination ... |

68 | On the Decidability of Metric Temporal Logic. In - Ouaknine, Worrell - 2005 |

50 | Decision problems for timed automata: A survey
- Alur, Madhusudan
- 2004
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Citation Context ...of an edge of the form (l , a, φ, pop, λ, l ′) is blocked if the stack is empty. Next, we consider the timed extension of an interesting subclass of pushdown automata called visibly pushdown automata =-=[5]-=-. A timed visibly pushdown automaton is a timed pushdown automaton for which the input alphabet Σ can be partitioned into three disjoint sets Σ = Σint∪Σcall∪Σret of internal, call, and return input sy... |

35 | On the language inclusion problem for timed automata: Closing a decidability gap
- Ouaknine, Worrell
- 2004
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Citation Context ...e system modelled by A. It was, however, recently proved that the language inclusion problem is decidable (albeit with non-primitive recursive complexity) if B is restricted to have at most one clock =-=[29]-=-. Another milestone in the success story of timed automata is the decidability of the model checking problem for timed automata and Metric Temporal Logic (MTL, for short) over finite timed words [30].... |

33 | A.: Reachability Games on Extended Vector Addition Systems with States
- Brázdil, Jančar, et al.
- 2010
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Citation Context ... value can be increased and decreased, there exists a successful run in which all accumulated weight values are never below zero. Similar problems have also been considered for untimed settings, eg., =-=[27,19,20,13]-=-. A timed automaton with discrete weights (dWTA, for short) is syntactically the same as a timed one-counter net. In the semantical graph induced by a dWTA, however, we allow the value of the counter ... |

21 | Pushdown timed automata: A binary reachability characterization and safety verification
- Dang
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Citation Context ...tisfiability of reachability properties for several subclasses of this model is decidable. Nine years later, it was shown that the binary reachability relation for timed pushdown systems is decidable =-=[14]-=-. Decidability of the reachability problem was also proved for several classes of timed counter systems [8], mainly by simple extensions of the classical region-graph construction [4]. The language in... |

16 | Model checking freeze LTL over one-counter automata.
- Demri, Lazic, et al.
- 2008
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Citation Context ...cessful run of A that w is associated with. Next we define some subclasses of timed pushdown automata; see also Fig. 1 for a graphical overview. We start with timed extensions of one-counter automata =-=[15,26]-=- and one-counter nets [23,1]. A timed one-counter automaton is a timed pushdown automaton where the stack alphabet is a singleton. By writing push and pop we mean that we increment and decrement the c... |

16 | DP lower bounds for equivalence-checking and model-checking of one-counter automata
- Jančar, Kučera, et al.
(Show Context)
Citation Context ...cessful run of A that w is associated with. Next we define some subclasses of timed pushdown automata; see also Fig. 1 for a graphical overview. We start with timed extensions of one-counter automata =-=[15,26]-=- and one-counter nets [23,1]. A timed one-counter automaton is a timed pushdown automaton where the stack alphabet is a singleton. By writing push and pop we mean that we increment and decrement the c... |

15 | Timed automata with observers under energy constraints
- Bouyer, Fahrenberg, et al.
- 2010
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Citation Context ...with Discrete Weights Next we will consider an interesting extension of lower-bound energy problems on weighted timed automata, introduced in [10], which gained attention in the last years, see, eg., =-=[11,31,9]-=-. In lower-bound energy problems, one is interested whether in a given automaton with some weight variable whose value can be increased and decreased, there exists a successful run in which all accumu... |

11 |
An infinite hierarchy of context-free languages
- Greibach
- 1969
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Citation Context .... the undecidability of the universality problem for pushdown automata. In fact, it has been long known that the universality problem is undecidable already for non-deterministic one-counter automata =-=[21,24]-=-. However, there are interesting decidability results for subclasses of timed pushdown automata: The language inclusion problem is decidable if A is a timed automaton, and B is a timed automaton with ... |

8 |
Jǐŕı Srba. Infinite runs in weighted timed automata with energy constraints
- Bouyer, Fahrenberg, et al.
- 2008
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Citation Context ... is decidable [15]. 4.6 Energy Problems on Timed Automata with Discrete Weights Next we will consider an interesting extension of lower-bound energy problems on weighted timed automata, introduced in =-=[10]-=-, which gained attention in the last years, see, eg., [11,31,9]. In lower-bound energy problems, one is interested whether in a given automaton with some weight variable whose value can be increased a... |

8 | Petri nets and regular processes
- Jančar, Esparza, et al.
- 1999
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Citation Context ...s decidable if only one clock is used. The language inclusion problem is also decidable if A is a one-counter net and B is a finite automaton, and if A is a finite automaton and B is a onecounter net =-=[25]-=-. This also implies the decidability of the universality problem for one-counter nets. Further we know that the universality and language inclusion problems are decidable if A and B are visibly pushdo... |

7 | Universality analysis for one-clock timed automata
- Abdulla, Deneux, et al.
(Show Context)
Citation Context ...there an error-free computation of C from (sI , ε) to (sF , x) for some x ∈M∗? The control state reachability problem is undecidable for channel machines, because channel machines are Turing-powerful =-=[12,2]-=-. The proof of Th. 1 is a reduction of the control state reachability problem for channel machines. The idea of the reduction is as follows: Given a channel machine C, we define a timed language L(C) ... |

7 |
Restricted one-counter machines with undecidable universe problems.
- Ibarra
- 1979
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Citation Context .... the undecidability of the universality problem for pushdown automata. In fact, it has been long known that the universality problem is undecidable already for non-deterministic one-counter automata =-=[21,24]-=-. However, there are interesting decidability results for subclasses of timed pushdown automata: The language inclusion problem is decidable if A is a timed automaton, and B is a timed automaton with ... |

6 | Undecidability of universality for timed automata with minimal resources
- Adams, Ouaknine, et al.
- 2007
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Citation Context ...some x ∈M∗ if, and only if, L(A) ∩ L(C) 6= ∅. 4.4 The Reduction Finally, we define a single-clock timed automaton B such that L(B) = TΣ+\L(C). The construction of B follows the same ideas as, eg., in =-=[3]-=-: B is the union of several single-clock timed automata, each of them violating one of the conditions of the definition of L(C). For instance, the timed automaton in Fig. 2 recognizes the set of timed... |

5 |
and Jiŕı Srba. Energy games in multiweighted automata
- Fahrenberg, Juhl, et al.
- 2011
(Show Context)
Citation Context ... value can be increased and decreased, there exists a successful run in which all accumulated weight values are never below zero. Similar problems have also been considered for untimed settings, eg., =-=[27,19,20,13]-=-. A timed automaton with discrete weights (dWTA, for short) is syntactically the same as a timed one-counter net. In the semantical graph induced by a dWTA, however, we allow the value of the counter ... |

4 | Lower-bound constrained runs in weighted timed automata
- Bouyer, Larsen, et al.
- 2012
(Show Context)
Citation Context ...with Discrete Weights Next we will consider an interesting extension of lower-bound energy problems on weighted timed automata, introduced in [10], which gained attention in the last years, see, eg., =-=[11,31,9]-=-. In lower-bound energy problems, one is interested whether in a given automaton with some weight variable whose value can be increased and decreased, there exists a successful run in which all accumu... |

4 | Optimal bounds for multiweighted and parametrised energy games
- Juhl, Larsen, et al.
- 2013
(Show Context)
Citation Context ... value can be increased and decreased, there exists a successful run in which all accumulated weight values are never below zero. Similar problems have also been considered for untimed settings, eg., =-=[27,19,20,13]-=-. A timed automaton with discrete weights (dWTA, for short) is syntactically the same as a timed one-counter net. In the semantical graph induced by a dWTA, however, we allow the value of the counter ... |

4 |
On the interval-bound problem for weighted timed automata
- Quaas
- 2011
(Show Context)
Citation Context ...with Discrete Weights Next we will consider an interesting extension of lower-bound energy problems on weighted timed automata, introduced in [10], which gained attention in the last years, see, eg., =-=[11,31,9]-=-. In lower-bound energy problems, one is interested whether in a given automaton with some weight variable whose value can be increased and decreased, there exists a successful run in which all accumu... |

2 | Simulation over onecounter nets is PSPACE-complete
- Hofman, Lasota, et al.
- 2013
(Show Context)
Citation Context ...sociated with. Next we define some subclasses of timed pushdown automata; see also Fig. 1 for a graphical overview. We start with timed extensions of one-counter automata [15,26] and one-counter nets =-=[23,1]-=-. A timed one-counter automaton is a timed pushdown automaton where the stack alphabet is a singleton. By writing push and pop we mean that we increment and decrement the counter, respectively, wherea... |

1 |
Rachid Echahed, and Riadh Robbana. On the automatic verification of systems with continuous variables and unbounded discrete data structures
- Bouajjani
- 1994
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Citation Context ...s of real-time systems, we have to ⋆ The author is supported by DFG, project QU 316/1-1. 2 Karin Quaas extend the model of timed automata with some unbounded discrete data structure. Bouajjani et al. =-=[7]-=- extended timed automata with discrete counters and a pushdown stack and proved that the satisfiability of reachability properties for several subclasses of this model is decidable. Nine years later, ... |

1 | Reachability in timed counter systems
- Bouchy, Finkel, et al.
(Show Context)
Citation Context ... it was shown that the binary reachability relation for timed pushdown systems is decidable [14]. Decidability of the reachability problem was also proved for several classes of timed counter systems =-=[8]-=-, mainly by simple extensions of the classical region-graph construction [4]. The language inclusion problem, however, was only considered in [18] for the class of timed pushdown systems. In [18] it i... |

1 |
and Rupak Majumdar. Decision problems for the verification of real-time software
- Emmi
- 2006
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Citation Context ...so proved for several classes of timed counter systems [8], mainly by simple extensions of the classical region-graph construction [4]. The language inclusion problem, however, was only considered in =-=[18]-=- for the class of timed pushdown systems. In [18] it is stated that the language inclusion problem is decidable if A is a timed pushdown automaton, and B is a single-clock timed automaton. The proof i... |

1 | Kleene algebras and semimodules for energy problems - Ésik, Fahrenberg, et al. - 2013 |

1 |
Model checking metric temporal logic over automata with one counter
- Quaas
- 2013
(Show Context)
Citation Context ...e counters. In fact, it is known that as soon as we add to MTL the capability to express restrictions on the values of a counter that can be incremented and decremented, model checking is undecidable =-=[32]-=-. Theorem 4. The model checking problem for timed visibly one-counter nets and MTL is undecidable, even if the timed visibly one-counter net does not use any clocks and is deterministic. Proof. We def... |