<p>You can take a look at the following paper:</p>

<p>Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers I: the power of interaction. J. ACM 39, 4 (Oct. 1992), 800-828. DOI= <a href="http://doi.acm.org/10.1145/146585.146599" rel="nofollow">http://doi.acm.org/10.1145/146585.146599</a></p>

<p>or the related paper:</p>

<p>Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers II: zero knowledge. J. ACM 39, 4 (Oct. 1992), 829-858. DOI= <a href="http://doi.acm.org/10.1145/146585.146601" rel="nofollow">http://doi.acm.org/10.1145/146585.146601</a></p>

CC BY-SA 2.5
2010-09-23T10:25:32.593Z
I've already gone through those papers and others by Condon, Lipton et al., but there's nothing there about the closure properties of these classes.
Cem Say
CC BY-SA 2.5
2010-09-23T12:38:39.617Z
@Cem: Can you clarify on the definition of "closure"? In particular, under what kind of operation do you seek closure?
Sadeq Dousti
CC BY-SA 2.5
2010-09-23T09:49:27.163Z
2010-09-23T09:49:27.163Z
Sadeq Dousti
<p>IP(2pfa) and AM(2pfa) are the classes of languages recognized with bounded error by private and public coin versions, respectively, of interactive proof systems with verifiers that are probabilistic finite automata with a two-way input head.</p>

<p>Are any closure properties of these classes known?</p>

<cc.complexity-theory><interactive-proofs>
closure properties of IP(2pfa) and AM(2pfa)
Cem Say
# closure properties of IP(2pfa) and AM(2pfa)

(Asked by: username_0 on 2010-09-23)

IP(2pfa) and AM(2pfa) are the classes of languages recognized with bounded error by private and public coin versions, respectively, of interactive proof systems with verifiers that are probabilistic finite automata with a two-way input head.

Are any closure properties of these classes known?

**Tags:** cc.complexity-theory, interactive-proofs

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## 1 answers

### Answer by username_1 on 2010-09-23. Score: 2

You can take a look at the following paper:

Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers I: the power of interaction. J. ACM 39, 4 (Oct. 1992), 800-828. DOI= <http://doi.acm.org/10.1145/146585.146599>

or the related paper:

Dwork, C. and Stockmeyer, L. 1992. Finite state verifiers II: zero knowledge. J. ACM 39, 4 (Oct. 1992), 829-858. DOI= <http://doi.acm.org/10.1145/146585.146601>

> **Comments:**
> **username_0**: I've already gone through those papers and others by Condon, Lipton et al., but there's nothing there about the closure properties of these classes.  
> **username_1**: @Cem: Can you clarify on the definition of "closure"? In particular, under what kind of operation do you seek closure?  

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