Probabilistic Game Automata

@inproceedings{Condon1986ProbabilisticGA,
  title={Probabilistic Game Automata},
  author={Anne Condon and Richard E. Ladner},
  booktitle={J. Comput. Syst. Sci.},
  year={1986}
}

Space-bounded probabilistic game automata

  • A. Condon
  • Computer Science, Mathematics
    JACM
  • 1991
TLDR
Any language recognizable in deterministic exponential time has an interactive proof that uses only logarithmic space, and it is shown that any language in BC-TIME(t(n)) has an Interactive proof that use time polynomial in t(n) but space only logARithmic in t (n).

On Probabilistic Quantified Satisfability Games

TLDR
The question for the case of threshold c=1 is completely answered, exhibiting that the case when ∀ is probabilistic is easier to decide than the remaining cases (PSPACE-complete).

A game-theoretic classification of interactive complexity classes

TLDR
This paper uses polynomially definable game systems to derive new characterizations of the complexity classes NEXP and coNEXP, and investigates the connection between game theory and interactive computation.

ON PROBABILISTIC QUANTIFIED SATISFIABILITY GAMES

We study the complexity of some new probabilistic variant of the problem Quantified Satisfiability(QSAT). Let a sentence ∃v1∀v2 . . . ∃vn−1∀vnφ be given. In classical game associated with the QSAT

On the power of finite automata with both nondeterministic and probabilistic states (preliminary version)

TLDR
It is shown that a language has constant l-tiling complexity if and only if it is regular, and the last lower bound follows by proving that the characteristic matrix of ever-y nonregular language has rank n for infinitely many n.

Computation of Equilibria in Noncooperative

TLDR
The main result is an algorithm for computing Sequential equilibrium, which is the most widely accepted notion of equilibrium (for mixed strategies of noncooperative probabilistic games) in mainstream economic game theory.

On the Complexity of Computational Problems Associated with Simple Stochastic Games (Extended Abstract)

TLDR
This work considers the computational complexity of simple stochastic games, a kind of two-person games under uncertainty, the original model of which was introduced in [L.A. Shapley, Proc. Nat. Acad. Sci. U.S.A., 39 (1953) 1095–1100].

Distinguishing tests for nondeterministic and probabilistic machines

TLDR
This work studies the problem of uniquely identifying the initial state of a given finite-state machine from among a set of possible choices, based on the input-output behavior, and provides optimal bounds for deciding whether such games have strategies winning with probability 1.

Tight Game Abstractions of Probabilistic Automata

TLDR
This work presents a new game-based abstraction technique for probabilistic automata (PA) that yields tighter upper and lower bounds on (extremal) reachability probabilities than state-based abstractions, showing the potential superiority over state- based abstraction of PA and Markov decision processes.

References

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  • Computer Science
    J. Comput. Syst. Sci.
  • 1984

Private coins versus public coins in interactive proof systems

TLDR
The probabilistic, nondeterministic, polynomial time Turing machine is defined and shown to be equivalent in power to the interactive proof system and to BPP much as BPP is the Probabilistic analog to P.

The Complexity of Logical Theories

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  • Mathematics, Computer Science
    Theor. Comput. Sci.
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Multiple-person alternation

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  • Computer Science
    20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
TLDR
This work generalizes the alternation machines of Chandra, Kozen and Stockmeyer and the private alternation Machines of Reif to model multiple person (team) games of incomplete information and characterization of certain time and space bounded versions of these machines demonstrate interesting relationships between ordinary time andspace hierarchies.

The knowledge complexity of interactive proof-systems

TLDR
A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.

Computational complexity of probabilistic Turing machines

TLDR
It is shown how probabilisticlinear-bounded automata can simulate nondeterministic linear-bounding automata and an example is given of a function computable more quickly by Probabilistic Turing machines than by deterministic Turing machines.

Finite Markov chains

TLDR
This lecture reviews the theory of Markov chains and introduces some of the high quality routines for working with Markov Chains available in QuantEcon.jl.