Paper Info
Title
One-Counter Verifiers for Decidable Languages.
Abstract
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 fixed-size 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 1-pebble probabilistic finite automata, i.e. they can recognize some nonstochastic languages with bounded error.
Year
DOI
Venue
2012
10.1007/978-3-642-38536-0_32
computer science symposium in russia
DocType
Volume
Citations 
Journal
abs/1207.3880
3
PageRank 
References 
Authors
0.46
20
1
Name
Order
Citations
PageRank
Abuzer Yakaryilmaz116825.31