Random generation of combinatorial structures from a uniform
Theoretical Computer Science
On dice and coins: models of computation for random generation
Information and Computation
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Domain Theory in Stochastic Processes
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
A testing scenario for probabilistic processes
Journal of the ACM (JACM)
Markovian workload modeling for Enterprise Application Servers
C3S2E '09 Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering
Hi-index | 0.00 |
Each probabilistic automaton M over an alphabet $\cal A$ defines a probability measure $\prob_M$ on the set of all finite and infinite words over $\cal A$. We can identify a k letter alphabet $\cal A$ with the set {0,1,…,k-1}, and, hence, we can consider every finite or infinite word w over $\cal A$ as a radix k expansion of a real number X(w) in the interval [0,1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x):=\prob_M{w : X(w)}. Utilizing the fixed--point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0,1] can be generated by a probabilistic automaton iff all the roots of F'(x)=0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.