On the power of randomized multicounter machines

Hromkovič, Juraj; Schnitger, Georg

doi:10.1016/j.tcs.2004.09.015

Cited by 3 publications

(2 citation statements)

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“…To our knowledge, 2pca's have never been investigated before. The only related work that we know is [11], in which Hromkovic and Schnitger examined two-way probabilistic multi-counter machines that are restricted to polynomial time, but, they did not present any result related to 2pca's. 2qca's, on the other hand, are examined only by Yamasaki at.…”

Section: Introductionmentioning

confidence: 96%

One-Counter Verifiers for Decidable Languages

Yakaryılmaz

2013

Computer Science – Theory and Applications

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Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working memory, i.e. replacing the working tape(s) with a single counter, we can define some IPS's for each decidable language. Such verifiers are called two-way probabilistic one-counter automata (2pca's). Then, we show that by adding a fixedsize quantum memory to a 2pca, called a two-way one-counter automaton with quantum and classical states (2qcca), the protocol can be space efficient. As a further result, if the 2qcca can use a quantum counter instead of a classical one, then the protocol can even be public, also known as Arthur-Merlin games.We also investigate the computational power of 2pca's and 2qcca's as language recognizers. We show that bounded-error 2pca's can be more powerful than their deterministic counterparts by giving a bounded-error simulation of their nondeterministic counterparts. Then, we present a new programming technique for bounded-error 2qcca's and show that they can recognize a language which seems not to be recognized by any bounded-error 2pca. We also obtain some interesting results for bounded-error 1-pebble quantum finite automata based on this new technique. Lastly, we prove a conjecture posed by Ravikumar (FSTTCS 1992) regarding 1pebble probabilistic finite automata, i.e. they can recognize some nonstochastic languages with bounded error.

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Section: Introductionmentioning

confidence: 96%

One-Counter Verifiers for Decidable Languages

Yakaryılmaz

2013

Computer Science – Theory and Applications

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“…Hromkovič and Schnitger compared the computational power of nondeterminism, randomization, and determinism for polynomial time counter machines [6].…”

Section: Introductionmentioning

confidence: 99%

Simulations by Time-Bounded Counter Machines

Petersen¹

2011

Int. J. Found. Comput. Sci.

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We investigate the efficiency of simulations of storages by several counters. A simulation of a pushdown store is described which is optimal in the sense that reducing the number of counters of a simulator leads to an increase in time complexity. The lower bound also establishes a tight counter hierarchy in exponential time.Then we turn to simulations of a set of counters by a different number of counters. We improve and generalize a known simulation in polynomial time. Greibach has shown that adding s + 1 counters increases the power of machines working in time n s . Using a new family of languages we show here a tight hierarchy result for machines with the same polynomial time-bound. We also prove hierarchies for machines with a fixed number of counters and with growing polynomial time-bounds.For machines with one counter and an additional "store zero" instruction we establish the equivalence of real-time and linear time. If at least two counters are available, the classes of languages accepted in real-time and linear time can be separated.

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Simulations by Time-Bounded Counter Machines

Petersen¹

2009

Developments in Language Theory

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On the power of randomized multicounter machines

Cited by 3 publications

References 25 publications

One-Counter Verifiers for Decidable Languages

One-Counter Verifiers for Decidable Languages

Simulations by Time-Bounded Counter Machines

Simulations by Time-Bounded Counter Machines

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