In this paper we analyze some features of the behaviour of quantum automata. In particular we prove that the class of languages recognized by quantum automata with isolated cut point is the class of reversible regular languages. As a more general result, we give a bound on the inverse error that implies the regularity of the language accepted by a quantum automaton.
In this paper we study the amount of secret information that must be given to participants in any secret sharing scheme that is secure against coalitious of dishonest participants in the model of Tompa and Woll [20]. \Ve show that any (k. n) threshold secret sharing algorithm in which any coalition of less than C participants has probability of successful cheating less than some E > 0 it must give to each participant shares xhose sizes are at least the size of the secret plus log f. { p (s) } , c s o n t h e set of secrets S and a sharing algorithm for secrets in S (both k n o w by each participant) naturally induce a probability distribution { p (d l ,. .. , d ,) } d ,~~~,. . ,~, E D , o n t h e joint space DI x. .. x D, of t h e possible values of the shares. Therefore, we will consider each D, a s a random variable. Formally, a (k , n) Threshold Secret Sharing Srherne is a method t o distribute shares t o t h e n participants such that: 'Partially supported by Italian Ministry of University and Research (b1.U.R.S.T.) and by National Council for Research (C.N.R.).
In this paper we consider the problem of identifying cheaters in secret sharing schemes. Rabin and Ben-Or presented a perfect and unconditionally secure secret sharing scheme in which the honest participants are able to identify the cheaters. We present a similar scheme, but one in which the information distributed to each participant is smaller.
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