Results 1  10
of
43
On the Undecidability of Probabilistic Planning and Related Stochastic Optimization Problems
 Artificial Intelligence
, 2003
"... Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the ..."
Abstract

Cited by 74 (0 self)
 Add to MetaCart
Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the world, namely that its information is complete and correct, and that the results of its actions are deterministic and known.
Recursive Markov decision processes and recursive stochastic games
 In Proc. of 32nd Int. Coll. on Automata, Languages, and Programming (ICALP’05
, 2005
"... Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural ..."
Abstract

Cited by 52 (11 self)
 Add to MetaCart
(Show Context)
Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural model for verification of probabilistic procedural programs and related systems involving both recursion and probabilistic behavior. RMCs define a class of denumerable Markov chains with a rich theory generalizing that of stochastic contextfree grammars and multitype branching processes, and they are also intimately related to probabilistic pushdown systems. RMDPs & RSSGs extend RMCs with one controller or two adversarial players, respectively. Such extensions are useful for modeling nondeterministic and concurrent behavior, as well as modeling a system’s interactions with an environment. We provide a number of upper and lower bounds for deciding, given an RMDP (or RSSG) A and probability p, whether player 1 has a strategy to force termination at a desired exit with probability at least p. We also address “qualitative ” termination questions, where p = 1, and model checking questions. 1
Probabilistic FiniteState Machines  Part I
"... Probabilistic finitestate machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition and machine translatio ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
Probabilistic finitestate machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition and machine translation are some of them. In part I of this paper we survey these generative objects and study their definitions and properties. In part II, we will study the relation of probabilistic finitestate automata with other well known devices that generate strings as hidden Markov models and ngrams, and provide theorems, algorithms and properties that represent a current state of the art of these objects.
Joint spectral characteristics of MATRICES: A CONIC PROGRAMMING APPROACH
, 2010
"... ..."
(Show Context)
Decidable and Undecidable Problems about Quantum Automata
 SIAM Journal on Computing
, 2005
"... We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. This result is in contrast with the correspondi ..."
Abstract

Cited by 23 (0 self)
 Add to MetaCart
(Show Context)
We study the following decision problem: is the language recognized by a quantum finite automaton empty or nonempty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds. This result is in contrast with the corresponding situation for probabilisticfinite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems.
Efficient algorithms for deciding the type of growth of products of integer matrices
, 2008
"... ..."
(Show Context)
Learning classes of probabilistic automata
 In COLT 2004, number 3120 in LNAI
, 2004
"... Abstract. Probabilistic finite automata (PFA) model stochastic languages, i.e. probability distributions over strings. Inferring PFA from stochastic data is an open field of research. We show that PFA are identifiable in the limit with probability one. Multiplicity automata (MA) is another device to ..."
Abstract

Cited by 15 (5 self)
 Add to MetaCart
(Show Context)
Abstract. Probabilistic finite automata (PFA) model stochastic languages, i.e. probability distributions over strings. Inferring PFA from stochastic data is an open field of research. We show that PFA are identifiable in the limit with probability one. Multiplicity automata (MA) is another device to represent stochastic languages. We show that a MA may generate a stochastic language that cannot be generated by a PFA, but we show also that it is undecidable whether a MA generates a stochastic language. Finally, we propose a learning algorithm for a subclass of PFA, called PRFA. 1
Rational stochastic language
 LIF  Université de Provence
, 2006
"... Abstract. The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K ∈ {Q, Q +, R, R +}. A rational stochastic language is a probability distribution over a free monoid Σ ∗ which is rational over K, that is which can be generat ..."
Abstract

Cited by 15 (7 self)
 Add to MetaCart
(Show Context)
Abstract. The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K ∈ {Q, Q +, R, R +}. A rational stochastic language is a probability distribution over a free monoid Σ ∗ which is rational over K, that is which can be generated by a multiplicity automata with parameters in K. We study the relations between the classes of rational stochastic languages S rat K (Σ). We define the notion of residual of a stochastic language and we use it to investigate properties of several subclasses of rational stochastic languages. Lastly, we study the representation of rational stochastic languages by means of multiplicity automata. 1
The Realization Problem for Hidden Markov Models: The Complete Realization Problem
 in Proc. 44th IEEE Conf. on Decision and Control and the European Control Conf
, 2005
"... Suppose m is a positive integer, and let M: = {1,...,m}. Suppose {Yt} is a stationary stochastic process assuming values inM. In this paper we study the question: When does there exist a hidden Markov model (HMM) that reproduces the statistics of this process? This question is more than forty years ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
Suppose m is a positive integer, and let M: = {1,...,m}. Suppose {Yt} is a stationary stochastic process assuming values inM. In this paper we study the question: When does there exist a hidden Markov model (HMM) that reproduces the statistics of this process? This question is more than forty years old, and as yet no complete solution is available. In this paper, we begin by surveying several known results, and then we present some new results that provide ‘almost ’ necessary and sufficient conditions for the existence of a HMM for a mixing and ultramixing process (where the notion of ultramixing is introduced here). In the survey part of the paper, consisting of Sections 2 through 8, we rederive the following known results: (i) Associate an infinite matrix H with the process, and call it a ‘Hankel ’ matrix (because of some superficial similarity to a Hankel matrix). Then the process has a HMM realization only if H has finite rank. (ii) However, the finite Hankel rank condition is not sufficient in general. There exist processes with finite Hankel rank that do not admit a HMM realization. (iii) An abstract necessary