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Page 1980 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
This book is an introduction to the theory of probabilistic automata and transformations of random sequences with different automata classes.  ...  Part 1 contains definitions of probabilistic automata and particular types of probabilistic automata.  ... 

Linear probabilistic sequential machines

R. Knast
1969 Information and Control  
Because linear probabilistic automata are a proper subclass of probabilistic automata, the question arises, whether linear probabilistic automata can accept nonregular events?  ...  In Section IV, it will be shown, that the proper subclass of probabilistic automata, i.e. the linear automata, contains the automata that accept nonregular events.  ... 
doi:10.1016/s0019-9958(69)90379-9 fatcat:su7ujs4egze3dj4sbfepfqa4zm

Page 2315 of Mathematical Reviews Vol. 48, Issue 6 [page]

1974 Mathematical Reviews  
G. 13528 Problems of synthesis of probabilistic transformers. (Russian. English summary) Probabilistic automata and their application (Russian), pp. 61-75. Izdat. “Zinatne”, Riga, 1971.  ...  The motiva- tion for the study of stochastic automata is derived from the need to describe and analyze system irregularities.  ... 

Page 1493 of Mathematical Reviews Vol. 58, Issue 2 [page]

1979 Mathematical Reviews  
Author’s summary: “We define and study deterministic automata with variable structure whose monitors are probabilistic automata.  ...  From the introduction: “We give the definition of a stochastic algebra and then restrict our attention to the special case of only unary operations, where we get stochastic automata with general state  ... 

Page 1776 of Mathematical Reviews Vol. 53, Issue 5 [page]

1977 Mathematical Reviews  
It is shown that the problem of transforming any class of random sequences by a class of automata can be reduced to transforming a class of Bernoulli sequences by another class of automata.  ...  Let n be the number of states of the automaton, p the number of input letters and / a parameter characterizing the probabilistic 94 INFORMATION AND COMMUNICATION, CIRCUITS, AUTOMATA 17% properties of the  ... 

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.  ...  Such an approach has been applied in the context of stochastic hybrid systems, in order to transform a model of a certain class of stochastic hybrid system to a model of an (ideally) easily-analysed class  ... 
doi:10.1007/978-3-319-22975-1_1 fatcat:gaosj6zatramnpqt246wibpt5i

Page 744 of Mathematical Reviews Vol. 38, Issue 4 [page]

1969 Mathematical Reviews  
problem for c-finite lan- Heller, Alex 4227 Probabilistic automata and stochastic transformations.  ...  If a stochastic transformation f on A(X x Y) has finite rank, an irredundant decomposition of f is a representation f=d: tf, where t,>0, >t,=1, and where each f, is a stochastic transformation on A(X x  ... 

Page 341 of Mathematical Reviews Vol. , Issue 80A [page]

1980 Mathematical Reviews  
Pohl, Hans W. 80a:68057 Analysis and synthesis of asynchronous stochastic automata. Found. Control Engrg. 3 (1978), no. 3, 119-123. The theorem of H.  ...  The author explains which transformations can be specified by circuit automata.  ... 

Page 982 of Mathematical Reviews Vol. 48, Issue 3 [page]

1974 Mathematical Reviews  
Makarevié, A general approach to the structural theory of probabilistic automata (pp. 55-59). III. Transformers: R. G. Buharaev, Problems of syn- thesis of probabilistic transformers (pp. 61-75); V.  ...  Gabbasov, On the characterization of the events that can be repre- sented by finite probabilistic automata (pp. 27-31); I. A, Metra, A stochastic counter (pp. 33-36). II.  ... 

Page 1476 of Automation and Remote Control Vol. 33, Issue 9 [page]

1972 Automation and Remote Control  
Here, however, we shall merely demonstrate the possibility of using applications of the theory of matrix spectra to probabilistic automata and trainability models.  ...  Under these conditions the system £ represents a certain semigroup of linear transformations of = and can be described by the system-stochastic matrices.  ... 

Page 1455 of Mathematical Reviews Vol. 52, Issue 4 [page]

1976 Mathematical Reviews  
The latter two automata are obtained from probabilistic automata essentially by replacing summation by maximum and product by minimum, and have been investigated by the author in a number of previous papers  ...  In this dissertation the author considers the stochastic sequential INFORMATION AND COMMUNICATION, CIRCUITS, AUTOMATA 52 ##10280-10284 machine in the form introduced by P. H.  ... 

Page 707 of Mathematical Reviews Vol. 58, Issue 1 [page]

1979 Mathematical Reviews  
The study of degenerate stochastic automaton characteristics and of the structure of elements from ©, +leads to a larger class of automata called quasi-degenerate stochastic automata.  ...  It is shown that in general the set of diagnostic experiments of probabilistic automata is not regular.  ... 

Page 301 of Mathematical Reviews Vol. 45, Issue 1 [page]

1973 Mathematical Reviews  
The input-output model is transformed to a unique canonical state-space form.  ...  G. 1702 Input-output modeling and identification of linear automata. Information Processing Lett. 1 (1971/72), 69-75.  ... 

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

1975 Mathematical Reviews  
First a pseudo-stochastic automaton is constructed and then the pseudo-stochastic automaton is transformed into a pure-stochastic one.  ...  Partitions that can be produced by probabilistic automata. (Russian. English summary) Probabilistic automata and their application (Russian), pp. 23-26. Izdat.  ... 

Exact and Approximate Abstraction for Classes of Stochastic Hybrid Systems

Jeremy Sproston
2014 Electronic Communications of the EASST  
A stochastic hybrid system contains a collection of interacting discrete and continuous components, subject to random behaviour.  ...  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  ...  As described in Section 1, when the heater is on, we consider that the rate of increase of the temperature is chosen from the normal distribution with mean 3.5 and standard deviation 1, truncated to the  ... 
doi:10.14279/tuj.eceasst.70.977 dblp:journals/eceasst/Sproston14 fatcat:5sz2klcszzd4pa4xl4zeuprsz4
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