## 50 Citations

### Space-bounded probabilistic game automata

- Computer Science, MathematicsJACM
- 1991

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

- MathematicsMFCS
- 2003

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

- Computer ScienceProceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference
- 1995

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

- Mathematics
- 2003

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)

- Computer ScienceSTOC '94
- 1994

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

- Computer Science, Economics
- 2000

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)

- Computer ScienceCOCOON
- 1996

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

- Computer Science, MathematicsSTOC '95
- 1995

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

- Computer ScienceCONCUR
- 2014

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

SHOWING 1-10 OF 14 REFERENCES

### The Complexity of Two-Player Games of Incomplete Information

- Computer ScienceJ. Comput. Syst. Sci.
- 1984

### Private coins versus public coins in interactive proof systems

- Computer ScienceSTOC '86
- 1986

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.

### Multiple-person alternation

- Computer Science20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979

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

- Mathematics, Computer ScienceSTOC '85
- 1985

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

- Computer ScienceSTOC '74
- 1974

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

- Mathematics
- 1960

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.