C. Dwork and L. Stockmeyer, On the power of 2-way Probabilistic Finite State Automata, Proc. FOCS 89 (1989) 480--485.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....recognizes a nonregular language with isolated cut point, then it requires time 2 n b infinitely often, for a positive constant b. Moreover, this time bound cannot be improved as shown by Kaneps and Freivalds [16] Dwork and Stockmeyer also considered the utilization of 2PFA s in cryptography [8, 9, 10]. They investigated interactive proof systems and zero knowledge interactive proof systems where the verifier is a 2PFA. 3 The Hadamard quotient Given a finite alphabet #, let # # , # be the free monoid generated by it. Given a semiring K,theclassK # # # of formal power series in ....

C. Dwork and L. Stockmeyer, On the power of 2-way Probabilistic Finite State Automata, Proc. FOCS 89 (1989) 480--485.

....abstract machines models (such as Turing machines) have provided a basis to study computational power. Restricted models have been used to gain insight in particular aspects of computation, such as Two way Probabilistic Finite Automata and Interactive Proof Systems to study randomization [9]. Note also the relevance of IPS to cryptography. We focus on an analysis of machine power from the restricted point of view of Finite Automata. Common to the de nitions of these machines are a nite set of states S = fs 0 ; s 1 ; s n g; a nite set of symbols (alphabet) an initial ....

....shown in [17] that 1PFA and 2PFA, with all real or all rational tran sition probabilities, accept the same classes of languages. As the language fa n b n jn 0g is accepted by a 2BPFA [13] the class of languages accepted by 2BPFA is larger than that of the 1PFA with isolated cut point. In [9] it is further shown that a 2PFA recognizing a non regular language (with bounded error probability) must use exponential expected time (for in nitely many inputs) Bounded error, polynomial expected time 2PFA are known to recognize only regular languages. An Interactive Proof Systems (IPS) for ....

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C. Dwork, L. Stockmeyer, \On the Power of 2-Way Probabilistic Finite State Automata ", Proc. of the 30th Annual Symposium on Foundations of Computer Science, 480-485, 1989.

....256 J. SHALLIT Example 2 Let L be the language of Example 1. Then it can be shown that N L (n) O( log n) 2 = log log n) Automaticity is a measure of descriptional complexity for languages, and was first studied (in a slightly different form) by Trakhtenbrot [29] Dwork and Stockmeyer [4, 5] used it (under the name nonregularity ) to prove that if a two way probabilistic finite automaton M recognizes a nonregular language with probability 1 2 ffi for some fixed ffi 0, then there exists a constant b such that M uses at least 2 n b expected time for infinitely many n. Similar ....

C. Dwork, L. Stockmeyer, On the power of 2-way probabilistic finite state automata. In: Proc. 30th Ann. Symp. Found. Comput. Sci. IEEE Press, 1989, 480--485.

....it was shown by Freivalds in [11] that the nonregular language fa m b m jm 1g could be recognized by a 2pfa with arbitrarily small error. However, the 2pfa s for fa m b m j m 1g defined by Freivalds require exponential expected time, and it was subsequently shown by Dwork and Stockmeyer [9, 10] that any 2pfa recognizing a non regular language with bounded error probability must take exponential expected time on infinitely many inputs. Thus, 2dfa s, 2nfa s and polynomial expected time, bounded error 2pfa s recognize exactly the regular languages. We show that 2qfa s are strictly more ....

C. Dwork and L. Stockmeyer. On the power of 2-way probabilistic finite state automata. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science, pages 480--485, 1989.

....from NSERC. being k automatic using the concept of automaticity studied in previous papers of the author and co authors [26, 27, 20, 10] In addition to its evident intrinsic interest, automaticity has proved useful in obtaining nontrivial lower bounds in computational complexity theory; see [7, 8, 16, 17]. More formally, define a deterministic finite automaton with output (DFAO) M to be a 6 tuple, Q; Sigma; ffi; q 0 ; Delta; where Q is a finite set of states, Sigma is a finite input alphabet, q 0 is the start state, and Delta is a finite output alphabet. The map ffi : Q Theta Sigma ....

C. Dwork and L. Stockmeyer. On the power of 2-way probabilistic finite state automata. In Proc. 30th Ann. Symp. Found. Comput. Sci., pages 480--485. IEEE Press, 1989.

....14] it was shown by Freivalds in [11] that the non regular language fa m b m jm 1g could be recognized by a 2pfa with arbitrarily small error. However, the 2pfa s for fa m b m g defined by Freivalds require exponential expected time, and it was subsequently shown by Dwork and Stockmeyer [9, 10] and independently by Kaneps and Freivalds [13] that any 2pfa recognizing a non regular language with bounded error probability must take exponential expected time on infinitely many inputs. Thus, 2dfa s, 2nfa s and polynomial expected time, bounded error 2pfa s recognize exactly the regular ....

C. Dwork and L. Stockmeyer. On the power of 2-way probabilistic finite state automata. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science, pages 480--485, 1989.

....the concept of automaticity: roughly speaking, how closely a formal language L can be approximated by regular languages L 0 ; also see Shallit Breitbart (1994) In addition to its evident intrinsic interest, automaticity has proved useful in obtaining nontrivial lower bounds. For example, in Dwork Stockmeyer (1989) , Dwork Stockmeyer (1990) and Kaneps Freivalds (1991) the measure was used to obtain lower bounds on computation by two way probabilistic finite automata. In Kaneps Freivalds (1990) it was used to obtain lower bounds on the space complexity of probabilistic Turing machines. In this paper, ....

C. Dwork and L. Stockmeyer, On the power of 2-way probabilistic finite state automata. In Proc. 30th Ann. Symp. Found. Comput. Sci. IEEE Press, 1989, 480-- 485.

.... a sequence is to being k automatic using the concept of automaticity studied in previous papers of the author and co authors [26, 27, 20, 10] In addition to its evident intrinsic interest, automaticity has proved useful in obtaining nontrivial lower bounds in computational complexity theory; see [7, 8, 16, 17]. More formally, define a deterministic finite automaton with output (DFAO) M to be a 6 tuple, Q; Sigma; ffi; q 0 ; Delta; where Q is a finite set of states, Sigma is a finite input alphabet, q 0 is the start state, and Delta is a finite output alphabet. The map ffi : Q Theta Sigma ....

C. Dwork and L. Stockmeyer. On the power of 2-way probabilistic finite state automata. In Proc. 30th Ann. Symp. Found. Comput. Sci., pages 480--485. IEEE Press, 1989.

....O(1) 3. AL (n) A L (n) 4. AL (n) 2 Sigma w2L Sigma n jwj. We now make the following Definition 8.1. Two strings w; w 0 are called n dissimilar for L if there exists a string v with jwvj; jw 0 vj n and either (i) wv 2 L, w 0 v 62 L; or (ii) wv 62 L, w 0 v 2 L. Then we have [36,50,94]: Theorem 8.1. AL (n) the maximum number of distinct pairwise n dissimilar strings for L. As an example, consider the language L = f0 n 1 n : n 0g: This language is clearly not regular. What is its automaticity It can be shown that the automaticity of L is AL (n) 2bn=2c 1 for n ....

....arithmetic progressions ( Linnik s Theorem ) Taking r = 2 n , the lemma implies that there are at least 2 n=43 n dissimilar strings for the language P R . Automaticity has been examined by Trakhtenbrot [100] Grinberg Korshunov [45] Karp [51] Breitbart [16,17,18] Dwork and Stockmeyer [36]; Kaneps Freivalds [50] Shallit Breitbart [93,94] Pomerance, Robson, Shallit [80] Glaister Shallit [42] and Shallit [92] Koskas and de Mathan (work in progress, 1996) show how to apply automaticity to obtain NUMBER THEORY AND FORMAL LANGUAGES 15 irrationality measures in finite ....

C. Dwork and L. Stockmeyer. On the power of 2-way probabilistic finite state automata. In Proc. 30th Ann. Symp. Found. Comput. Sci., pages 480--485. IEEE Press, 1989.

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