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Verification and Control of Probabilistic Rectangular Hybrid Automata [chapter]

Jeremy Sproston
2015 Lecture Notes in Computer Science  
We highlight the differences between verification and control problems for probabilistic rectangular hybrid automata and the corresponding problems for non-probabilistic rectangular hybrid automata.  ...  Finally, we will also consider how probabilistic rectangular hybrid automata can be used as abstract models for more general classes of stochastic hybrid systems.  ...  In [32] , a "symbolic" search through the state space using non-probabilistic methods is performed first, after which a finite-state Markov decision process is constructed and analysed.  ... 
doi:10.1007/978-3-319-22975-1_1 fatcat:gaosj6zatramnpqt246wibpt5i

Exact and Approximate Abstraction for Classes of Stochastic Hybrid Systems

Jeremy Sproston
2014 Electronic Communications of the EASST  
The formal verification of a stochastic hybrid system often comprises a method for the generation of a finite-state probabilistic system which either represents exactly the behaviour of the stochastic  ...  Firstly, we generalise previous results by showing how bisimulation-based abstractions of non-probabilistic hybrid automata can be lifted to the setting of probabilistic hybrid automata, a subclass of  ...  Example: Faulty Thermostat We now illustrate the approximate analysis method proposed in the previous section with an application to the PRA model of a faulty thermostat presented in Figure 1 .  ... 
doi:10.14279/tuj.eceasst.70.977 dblp:journals/eceasst/Sproston14 fatcat:5sz2klcszzd4pa4xl4zeuprsz4

Page 700 of Mathematical Reviews Vol. 44, Issue 3 [page]

1972 Mathematical Reviews  
3800-3806 method for constructing these memory automata on universal elements that realize the function Either-Or.  ...  A decomposition method for the structural synthesis of finite automata. I, II. (Russian.  ... 

An extension of the inverse method to probabilistic timed automata

Étienne André, Laurent Fribourg, Jeremy Sproston
2012 Formal methods in system design  
The method relies on parametric analysis of a nonprobabilistic version of the probabilistic timed automata model using the "inverse method".  ...  Probabilistic timed automata can be used to model systems in which probabilistic and timing behavior coexist.  ...  Construct the non-probabilistic version A * of A . 2. Construct K 0 for A * using the classical inverse method.  ... 
doi:10.1007/s10703-012-0169-x fatcat:mdza2juovfeffkvppcslmjrdzm

Probabilistic Model Checking of Deadline Properties in the IEEE 1394 FireWire Root Contention Protocol

Marta Kwiatkowska, Gethin Norman, Jeremy Sproston
2003 Formal Aspects of Computing  
Probabilistic timed automata are used to formally model and verify the protocol against properties which require that a leader is elected before a deadline with a certain probability.  ...  We present a formal verification of the protocol using probabilistic model checking. Rather than analyze the functional aspects of the protocol, by asking such questions as "will a leader be elected?"  ...  The verification used a variety of techniques, including high-level abstraction and methods for the construction of finite-state probabilistic systems using explorative algorithms, region equivalence,  ... 
doi:10.1007/s001650300007 fatcat:j44aupeidjbfdexwe3eaxlzrsm

Ultrametric Finite Automata and Their Capabilities

Maksims Dimitrijevs, Kristīne Cīpola
2016 Baltic Journal of Modern Computing  
Previous research has shown that ultrametric automata can recognize complex languages and can have small number of states when classical automata require much more states.  ...  Ultrametric automata use p-adic numbers to describe the random branching of the process of computation.  ...  that languages recognizable by these probabilistic finite automata are the same as for ordinary probabilistic finite automata.  ... 
doi:10.22364/bjmc.2016.4.4.19 fatcat:dud35ixagjhqbeosca3em33iky

An MTBDD-Based Implementation of Forward Reachability for Probabilistic Timed Automata [chapter]

Fuzhi Wang, Marta Kwiatkowska
2005 Lecture Notes in Computer Science  
In this paper we propose an encoding method for Probabilistic Timed Automata (PTA) based on MTBDDs.  ...  Our key contribution is a general placeholder encoding method for Probabilistic Timed Automata and an experimental MTBDD-based model checker which has been partly integrated with PRISM.  ...  We would like to thank the authors of the DDD library for letting us use their DDD implementation. We would also like to thank Gethin Norman and David Parker for helpful discussion.  ... 
doi:10.1007/11562948_29 fatcat:3mauljrh3jgw5k65z6kzo4fx6m

Computability of Logical Neural Networks

T.B. Ludermir
1992 Journal of Intelligent Systems  
This new method increases the computability power of such networks beyond that of finite state acceptors.  ...  We studied the computability of networks of PLNs (Probabilistic Logic Node (Aleksander, 1988)). We suggested a new method of recognition based on stored probabilities with PLN networks.  ...  Automata Theory Although the literature on deterministic and non-deterministic automata is quite substantial, not quite as much work has been done on probabilistic automata (Rabin, 1963) .  ... 
doi:10.1515/jisys.1992.2.1-4.261 fatcat:kod2o5tqi5as5dmd3i6ymixs6a

Page 6451 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
We give algorithms for constructing finite automata which represent integer sets that satisfy linear constraints.  ...  probabilistic 1/O automata and its relationship to probabilistic bisimulation.  ... 

Symbolic Computation of Maximal Probabilisti Reachability [chapter]

Marta Kwiatkowska, Gethin Norman, Jeremy Sproston
2001 Lecture Notes in Computer Science  
As in the non-probabilistic case, our state space exploration algorithm is semi-decidable for infinite-state systems.  ...  We illustrate our approach with examples of probabilistic timed automata, for which previous approaches to this reachability problem were either based on unnecessarily fine subdivisions of the state space  ...  Two verification methods for probabilistic timed automata are presented in [15] .  ... 
doi:10.1007/3-540-44685-0_12 fatcat:pwmnsjbtnzc4venxbjbceqoxae

Page 247 of Mathematical Reviews Vol. 46, Issue 1 [page]

1973 Mathematical Reviews  
The coverage problem for an arbitrary non- deterministic finite automaton is replaced by a series of monotypical problems for nondeterministic automata of a special chain structure.  ...  , and then to construct such a deterministic finite automaton if one exists.  ... 

Page 2061 of Mathematical Reviews Vol. 57, Issue 5 [page]

1979 Mathematical Reviews  
Rabin-Scott model, ie., there are quasi-initialised finite automata which have fewer states than any finite automaton for the same language.  ...  Bounds on the number of states and on decision procedures for quasi-initialised finite automata are studied.  ... 

Page 2193 of Mathematical Reviews Vol. 50, Issue 6 [page]

1975 Mathematical Reviews  
Partitions that can be produced by probabilistic automata. (Russian. English summary) Probabilistic automata and their application (Russian), pp. 23-26. Izdat.  ...  J. 16176 Method for state reduction of automata taking into account tech- nical peculiarities of synchronous and asynchronous operational modes. German and Russian summaries) Automatica—J.  ... 

Model-checking branching-time properties of probabilistic automata and probabilistic one-counter automata [article]

T. Lin
2021 arXiv   pre-print
And then, for each probabilistic automata, by constructing a probabilistic one-counter automaton with the same behavior as questioned probabilistic automata the undecidability of model-checking problems  ...  We first show, by reducing to emptiness problem of probabilistic automata, that the model-checking of probabilistic finite automata against branching-time temporal logics are undecidable.  ...  With the Theorem 1.1 in place, we construct, for each probabilistic finite automaton, a probabilistic one-counter automaton. Herein, we show next the main result Theorem 1.2.  ... 
arXiv:1502.07549v2 fatcat:zmyi6hugozdhza3y7blvnu5lyy

Decidable and undecidable problems about quantum automata [article]

Vincent D. Blondel, Emmanuel Jeandel, Pascal Koiran, Natacha Portier
2003 arXiv   pre-print
This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and non-strict thresholds both lead to undecidable problems.  ...  We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty?  ...  Acknowledgment P.K. would like to thank Etienne Ghys for pointing out reference [OV90] .  ... 
arXiv:quant-ph/0304082v1 fatcat:ofivd7nigjfj5ng66fvtkf75ym
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