J. Hartmanis; On non-determinancy in simple computing devices, Acta Informatica 1 (1972), 336-344  Home/Search   Document Not in Database   Summary   Related Articles   Check

....transducers. Related results hold in the nondeterministic case. 1 Introduction Two way nite automata with a pebble recognize regular languages only [3] With more than one pebble they are equivalent to the multihead nite automata, which recognize all logarithmic space languages, see, e.g. [17, 24, 26]. Recently, it has been shown that restricting the pebbles to have nested life times, the two way pebble automata still recognize regular languages only [15] and this also holds when generalized to trees [8] Even more recently, a corresponding tree transducer model was proposed as a general model ....

J. Hartmanis; On non-determinancy in simple computing devices, Acta Informatica 1 (1972), 336-344

....Re lated results hold in the nondeterministic case. 1 Introduction Two way finite automata with a pebble recognize regular languages only [3] With more than one pebble they are equivalent to the multihead finite automata, which recognize all logarithmic space languages, see, e.g. [17,24,26]. Recently, it has been shown that restricting the pebbles to have nested life times, the two way pebble automata still recognize regular languages only [15] and this also holds when generalized to trees [8] Even more recently, a corresponding tree trans ducer model was proposed as a general ....

J. Hartmanis; On non-determinancy in simple computing devices, Acta Informatica 1 (1972), 336-344

....or may change to the initial contents (returning strategy) In a centralized system only a distinguished component (the master) is allowed to ask the stack contents of any other component. Note here the differences between these systems and other mechanisms like multi head pushdown automata [8, 9], multi stack pushdown automata or multi push down automata [2] We compare the devices introduced here with all aforementioned devices from the point of view of their computational power. The paper is organized as follows. The next section gives the definitions of parallel communicating pushdown ....

....A = k; Q; V; Delta; f; q 0 ; Z 0 ; F ) where Q; V; Delta; q 0 ; Z 0 ; F have the same meaning as for a usual pushdown automaton, and f is a mapping from Q Theta (V [ f g) k Theta Delta into the set of finite subsets of Q Theta Delta . The above definition is similar to the one found in [8] and [9] Thus, q; x) 2 f(s; a 1 ; a 2 ; a k ; A) indicates that the automaton in state s, with symbol A on the top of its stack, the ith head reading a i may enter state q and write x in the pushdown memory. The input heads may pass over one another freely and they are prevented from ....

J. Hartmanis, "On nondeterminancy in simple computing devices," Acta Informatica 1 (1972) 336--344.

....CFL s. In order to show that any language in SAC 1 is recognized by uniform programs over a groupoid, we simply observe that Sudburough s logspace reduction from a language recognized by an AuxNPDA to a context free language is a uniform projection. Recall the main steps of the proof. Step 1 ([37]) We know that if L 2 LOGCFL, then it is recognized by an AuxNPDA M in space c log n and polynomial time. This machine can be simulated by a multiple head PDA M 1 (i.e. constant working space) the working tape of M is divided into c blocks of size log n; the content of each block is represented ....

J. Hartmanis, On the Non-Determinancy in Simple Computing Devices, Acta Informatica 1,pp.336-344, 1972.

.... nondeterministic multihead twoway and one way finite automata, connections between multihead two way finite automata and the corresponding log space Turing machines, and transformations of languages recognized by one type of devices to languages recognized by the same or different types of devices [Ha72], Ib73] Su75] Mo76] Se77a] Se77b] YR78] Mo80] More specifically, it was proven that the log space deterministic and nondeterministic complexity classes L and NL can be represented as proper hierarchies defined by deterministic and respectively nondeterministic multihead two way finite ....

.... was also shown that the heads hierarchies for multihead one way deterministic and nondeterministic finite automata are proper [YR78] These decomposition, separation and reduction properties are related to the longstanding open problem, What is the smallest ff such that NL ae Dspace(log ff n) [Ha72][Su75] Although in the last 20 years probabilistic computation has continuously been an active topic in computational complexity, probabilistic analogues of these results have not been reported. Our goal is to study properties of multihead two way probabilistic finite automata in connection with ....

[Article contains additional citation context not shown here]

Hartmanis, J. On Non-Determinancy in Simple Computing Devices. Acta Informatica 1, 1972, pp. 336-344

....by using logarithmic space to generate, on demand, the symbols produced by the logspace transformation. As to the inclusion from left to right, the proofs are almost identical for the two MetaTheorems. So, we will present only the proof of MetaTheorem 1. By using a technique presented by Hartmanis [Har72], one can show that logarithmic space can be simulated, with only polynomial time loss, by multihead finite state automata and vice versa. See [Mac94b, Mac94a] for the corresponding adaptations to the settings of probabilistic and probabilistic plus nondeterministic computation. Then we have ....

J. Hartmanis. On non-determinancy in simple computing devices. Acta Informatica, 1:336--344, 1972.

....to increase storage density [SHL65] That the difference is real becomes apparent in other contexts, however for example, when we work with the corresponding multihead finite automata rather than with logarithmic space bounded Turing machines. The latter are collectively equivalent to the former [Ha72]; but doubling the space corresponds, roughly, to doubling the number of heads, a resource that definitely cannot be so reduced [Se77, Mo80] We show below that Gill s result can be tightened, really to require no extra space, and to hold even at sublogarithmic levels, at least if the space bounds ....

J. Hartmanis, On non-determinancy in simple computing devices, Acta Informatica 1, 4 (1972), 336--344.

.... = S 1 k=1 AM(2pfa(k) AM poly (log n) S 1 k=1 AM poly (2pfa(k) UAM(logn) S 1 k=1 UAM(2pfa(k) UAM poly (log n) S 1 k=1 UAM poly (2pfa(k) Theorem 2) The proofs of these relations can be easily obtained by adapting the proofs of their deterministic and nondeterministic versions [Ha72]. ffl For multihead two way unbounded and one sided error probabilistic finite automata, the heads hierarchies are proper, i.e. for k 1, 2PFA(k) 2PFA(k 1) 2PFA poly (k) 2PFA poly (k 1) Theorem 5) and 2RPFA(k) 2RPFA(k 1) Theorem 6) For k 2 the separations are over one letter ....

.... (Theorem 11) For log space unbounded error complexity classes the log space reductions are even stronger: PL log 1PFA(2) PL log 1PCM(1) Theorem 10) and P = UAM(logn) log UAM(1pfa(2) P log UAM(1pcm(1) Theorem 11) Nondeterministic versions of these theorems were proven by Hartmanis [Ha72] and Sudborough [Su75] ffl The completeness result for PL (Theorem 10) induces probabilistic variants of Savitch s maze threading problem that surprisingly, have not been remarked so far. Note that several (nondeterministic) variants of maze threading problems were already known in early ....

[Article contains additional citation context not shown here]

Hartmanis, J. On Non-Determinancy in Simple Computing Devices. Acta Informatica 1, 1972, pp. 336-344

....Grant No. CDA 8822724. 1 Background It is known that the heads of multihead (deterministic and nondeterministic) finite automata represent a storage alternative to the work tape of (deterministic and nondeterministic) logarithmic space Turing machines. These results were noted in early 70 s [Har72]. In this paper we show that similar relations hold in the setting of probabilistic computation, i.e. the class of languages recognized by logspace (unbounded error, bounded error, one sidederror) probabilistic Turing machines can be characterized in terms of the classes of languages recognized by ....

....probability 1. By ae and we mean proper inclusion and inclusion (possibly not proper) respectively. kAk denotes the norm of the n by n matrix A defined by kAk = max i P n j=1 ja ij j, and N is the set of natural numbers. 2 Connections among probabilistic automata In early 70 s, Hartmanis [Har72] proved the relation : S 1 k=1 kNFA = Nspace(log n) connecting the number of heads of multihead nondeterministic finite automata to the work space of logarithmic space nondeterministic Turing machines. By adapting his technique to the setting of probabilistic computation, similar relations can ....

Hartmanis, J. On Non-Determinancy in Simple Computing Devices. Acta Informatica 1, 1972, pp. 336-344.

No context found.

J. Hartmanis. On non-determinancy in simple computing devices. Acta Informatica, 1:336--344, 1972.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC