The complexity of the max word problem and the power of one-way interactive proof systems

Condon, Anne

doi:10.1007/bf01271372

Cited by 23 publications

(11 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A one-way interactive proof system [Con93a] is an IPS where the prover is restricted so that it maps the set of input strings to the set of sequences from the communication alphabet.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Finite state verifiers with constant randomness

Say¹,

Yakaryılmaz²

2014

Logical Methods in Computer Science

View full text Add to dashboard Cite

Abstract. We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers. A corollary of our main result is that the class of outcome problems corresponding to O(log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals NL.

show abstract

“…A one-way interactive proof system [Con93a] is an IPS where the prover is restricted so that it maps the set of input strings to the set of sequences from the communication alphabet.…”

Section: Preliminariesmentioning

confidence: 99%

“…Relaxing the randomness bound of the one-way IPS further does not help on its own, since [Con93a] oneway-IP(poly-time, log-space) = NP, (2.4) but allowing interaction as well famously yields [Con91,Sha92] IP(poly-time, log-space) = PSPACE. (2.5)…”

Section: Preliminariesmentioning

confidence: 99%

Finite state verifiers with constant randomness

Say¹,

Yakaryılmaz²

2014

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…BenOr, Goldwasser, Kilian and Wigderson [9] extended these ideas to define a notion of multi-prover interactive proofs. Applications of interactive proof based ideas to the derivation of hardness of approximation results emerged in the work of Condon [11] and Feige, Goldwasser, Lovász, Safra and Szegedy [15]. The latter showed that the size of a maximum independent set in a graph is hard to approximate.…”

Section: Background Techniques and Related Workmentioning

confidence: 99%

The Complexity of Approximating a Nonlinear Program

Bellare

Rogaway²

1993

Complexity in Numerical Optimization

View full text Add to dashboard Cite

We consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope. We show that there is no polynomial time approximation algorithm for this problem, even one with a very poor guarantee, unless P = NP. We show that even when the polynomial is quadratic (i.e. quadratic programming) there is no polynomial time approximation unless NP is contained in quasi-polynomial time.Our results rely on recent advances in the theory of interactive proof systems. They exemplify an interesting interplay of discrete and continuous mathematics-using a combinatorial argument to get a hardness result for a continuous optimization problem.

show abstract

“…(See for example [5], [SI or [SI). Condon [3] previously studied log-space, "one-way" interactive proof systems, in which the Verifier never writes on the communication cell. A one-way interactive proof system is a special case of a private interactive proof system with the poly-tree-size restriction.…”

Section: Related Workmentioning

confidence: 99%

“…In previous work, Condon [3] showed that NP IP(1og-space), even when the Verifier runs in polynomial time. However, the Verifier could use polynomially many random bits.…”

Section: Lemma 1 Ip(1og-space Poly-tree-size) G Npmentioning

confidence: 99%

Interactive Proof Systems with Polynomially Bounded Strategies

Condon

Ladner

1995

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Interactive proof systems in which the Prover is restricted to have a polynomial size strategy are investigated. The restriction of polynomial size computation tree, or logarithmically bounded number of coin flips, guarantee a polynomial size strategy. One result is that interactive proof systems in which the Prover is restricted to a polynomial size strategy are equivalent to MA, Merlin-Arthur games, of Babai and Moran [l]. Polynomial tree size is also equivalent to MA, but when logarithmic space is added as a restriction, the power of polynomial tree size reduces to NP. A logarithmic number of coin flips is equivalent to NP, even when logarithmic space is added as a restriction.

show abstract

The complexity of the max word problem and the power of one-way interactive proof systems

Cited by 23 publications

References 18 publications

Finite state verifiers with constant randomness

Finite state verifiers with constant randomness

The Complexity of Approximating a Nonlinear Program

Interactive Proof Systems with Polynomially Bounded Strategies

Contact Info

Product

Resources

About