On the Power of Finite Automata with Both Nondeterministic and Probabilistic States

@article{Condon1998OnTP,
  title={On the Power of Finite Automata with Both Nondeterministic and Probabilistic States},
  author={Anne Condon and Lisa Hellerstein and Samuel Pottle and Avi Wigderson},
  journal={SIAM J. Comput.},
  year={1998},
  volume={27},
  pages={739-762}
}
We study finite automata with both nondeterministic and random states (npfa's). We restrict our attention to those npfa's that accept their languages with a small probability of error and run in polynomial expected time. Equivalently, we study Arthur--Merlin games where Arthur is limited to polynomial time and constant space. Dwork and Stockmeyer [SIAM J. Comput., 19 (1990), pp. 1011--1023] asked whether these npfa's accept only the regular languages (this was known if the automaton has only… 

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References

SHOWING 1-10 OF 31 REFERENCES

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.

A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata

It is shown that if a two-way probabilistic finite-state automaton (2pfa) M recognizes a nonregular language L with error probability bounded below $\frac{1}{2}$, then there is a positive constant b

Running Time to Recognize Nonregular Languages by 2-Way Probabilistic Automata

TLDR
The running time for the recognition of nonregular 2-dimensional languages by 4-way pfa can be essentially smaller, namely, linear.

A Lower Bound for Probabilistic Algorithms for Finite State Machines

Probabilistic Game Automata

Finite state verifiers I: the power of interaction

TLDR
An investigation of interactive proof systems (IPSs) where the verifier is a 2-way probabilistic finite state automaton (2pfa) is initiated, and it is shown that IPSs with verifiers in the latter class are as powerful as IPSs where verifiers are polynomial-time Probabilistic Turing machines.

Automaticity: Properties of a Measure of Descriptional Complexity

TLDR
The notion of automaticity is explored, which attempts to model how “close” f is to a finite-state function.

Computational models of games

  • A. Condon
  • Computer Science
    ACM distinguished dissertations
  • 1989
TLDR
A new computational model of two person games, called a probabilistic game automaton, is defined and a number of new results on the power of the space bounded analogues of Arthur-Merlin games and interactive proof systems are proved.

Proof verification and hardness of approximation problems

TLDR
The authors improve on their result by showing that NP=PCP(logn, 1), which has the following consequences: (1) MAXSNP-hard problems do not have polynomial time approximation schemes unless P=NP; and (2) for some epsilon >0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup ePSilon / unless P =NP.

Lower bounds by probabilistic arguments

  • A. Yao
  • Computer Science, Mathematics
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
TLDR
It is proved that, to compute the majority function of n Boolean variables, the size of any depth-3 monotone circuit must be greater than 2nε, and thesize of any width-2 branching program must have super-polynomial growth.