W. Masek, A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of linear length, even with nondeterministic AND, OR, or PARITY nodes. There has also been great success in proving lower bounds on the size of read once programs. Many of the functions that require exponential size are very simple; some are easily computed with mere read twice programs. Masek [Ma76] was the first to consider read once programs, proving a lower bound of Omega Gamma m ) on the size of any program determining whether x i = m. Zak [Za84] and later Wegener [We88, We87] proved lower bounds of 2 Omega Gamma for the function CLIQUE of determining whether a graph on n ....

W. Masek. A Fast Algorithm for the String-Editing Problem and Decision Graph Complexity. SM Thesis, MIT, 1976.

..... We hope that it will be possible to eliminate this width bound altogether. 2 1.3. Limited reading A read k times only branching program is allowed to encounter each variable at most k times along any computation path. This hierarchy of classes of branching programs was introduced by Masek [Ma]. Wegener [We] conjectures an exponential gap between the levels of this hierarchy and gives candidate Boolean functions computable with polynomial size read k times only programs but conjectured to require exponential size read (k Gamma 1) times only programs. No superpolynomial lower bounds ....

....time decidable (recognizing the graphs that consist of a clique of size v=2 and v=2 isolated vertices. We shall improve the lower bound to C n (for a different function, also a polynomial time decidable graph property) Section 3) 3 1.4. Space complexity: the eraser RAM It has been noted ([Ma], BFKLT] Pu] that a lower bound S(n) on the size of the smallest branching program computing a Boolean function f n of n variables implies an Omega Gamma 47 S(n) lower bound on the space complexity of the family f f n : n = 1; 2; g on any reasonable model of computation. The ....

W. Masek, A fast algorithm for the string editing problem and decision graph complexity, M.Sc. Thesis, MIT 1976

....read once programs have been considered by some researchers for possible use in hardware verification [GM94] Very little was known about the complexity of multiplication. There has been great success in proving lower bounds on the size of read once programs, even for some very simple functions [Ma76, Du85, Za84, We87, SS93]. For example, it was proved in [Za84] see also [We87] that determining whether a graph on n nodes is an n 2 clique (with no further edges) requires size 2## n) Until the time of this writing, the only asymptotically optimal lower bound was found in [BHST87] which proves a bound of 2 ## n ....

W. Masek, A Fast Algorithm for the String-Editing Problem and Decision Graph Complexity, SM Thesis, MIT, Cambridge, MA, 1976.

....reasons to assume that such a result would yield important new insights into the general nature of lower bound proofs. 5 1.2.2 General Branching Programs Now we are ready to define the most fundamental model of computation for this work. The original definition goes back to Lee [71] and Masek [73]. Definition 1.5: A branching program (BP) on the variable set fx 1 ; x n g is a directed acyclic graph with one source and sinks labeled by the constants 0 or 1, resp. Each non sink node is labeled by a variable x i and has exactly two outgoing edges labeled by 0 or 1, resp. This graph ....

W. Masek. A Fast Algorithm for the String Editing Problem and Decision Graph Complexity. M. Sc. Thesis, MIT, Dept. of EECS, May 1976.

....In order to learn more about the power of branching programs, various restricted models were investigated. One of the most intensively studied was that of read k times programs (k b.p. or k n.b.p. where in each computation every input bit can be tested at most k times. This model introduced in [10] corresponds to so called eraser Turing machines, and the first super polynomial lower bounds for 1 b.p. were obtained in [19, 18] see also [3, 6, 1, 8] for further results in that direction. Exponential lower bounds for 1 n.b.p. were proven in [4, 7, 2, 5] However, any attempts to get such ....

W. Masek, A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.

....Complexity, lower bounds, branching programs, switching and rectifier networks, corrupting machines Warning: Essentially this paper will be published in Discrete Applied Mathematics and will hence be subject to copyright restrictions. It is for personal use only. 1 Supported by DFG grant Me 1077 10 1. 2 Supported by grant # 96 01 01222 of the Russian Basic Research Foundation, and by an AMS FSU grant. 1 Introduction We consider the usual model of branching programs (b.p. This model captures in a natural way the deterministic space whereas nondeterministic branching programs ....

....Complexity, lower bounds, branching programs, switching and rectifier networks, corrupting machines Warning: Essentially this paper will be published in Discrete Applied Mathematics and will hence be subject to copyright restrictions. It is for personal use only. 1 Supported by DFG grant Me 1077 10 1. 2 Supported by grant # 96 01 01222 of the Russian Basic Research Foundation, and by an AMS FSU grant. 1 Introduction We consider the usual model of branching programs (b.p. This model captures in a natural way the deterministic space whereas nondeterministic branching programs (n.b.p. ....

[Article contains additional citation context not shown here]

W. Masek, A fast algorithm for the string editing problem and decision graph complexity, Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.

....Let us briefly sketch the progress in that direction (see, e.g. 14] for more comprehensive survey) One of the most intensively studied models was that of read k times programs (kb. p. or k n.b.p. where in each computation every input bit can be tested at most k times. This model introduced in [9] corresponds to so called eraser Turing machines, and the first super polynomial lower bounds for 1 b.p. were obtained in [19, 18] In fact, for a related model of regular resolution (this is a 1 b.p. with more than two outputs) exponential lower bounds were proved, already 30 years ago, by ....

W. Masek, A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.

....Meinel (1992) We now review some of the main results that are relevant to understanding the structure. Read Once Decision Graphs Wegener (1987) proved that the class of polynomially sized read once decision graphs is a strict subset of the class of polynomially sized read twice decision graphs. Masek (1976) gives an ingenious example, attributed to Michael Fredman, where reading features more than once can be useful in reducing the size of the decision graph for a natural function. A sketch of the idea is given in the example below. CHAPTER 6. OBLIVIOUS READ ONCE DECISION GRAPHS 152 Example 6.1 ....

....more powerful than read once) Let f be the function that is one iff the sum of the n input bits is m. It can be shown that a read once decision graph must have at least m(n Gamma m 1) 2 nodes in the graph because the function must update the count of ones (0 to m) each time a feature is read (Masek 1976). If at any interior level (excluding the top m and bottom log 2 m) there are less than m nodes, then they cannot represent the sum of ones, and the graph cannot compute the correct function. If, however, input features can be read multiple times, then the following scheme can be used. The ....

[Article contains additional citation context not shown here]

Masek, W. J. (1976), A fast algorithm for the string editing problem and decision graph complexity, Master's thesis, Massachusetts Institute of Technology.

.... studied in the hope of separating some complexity classes and for studying the amount of space needed to compute various functions [4] Two important theorems tell us that an algorithm in SPACE(S(n) for S(n) log n has a branching program complexity of at most c S(n) for some constant c [16], and that constant width branching programs are very powerful, being able to accept all NC 1 languages [2] In the machine learning community, general decision graphs were investigated by Oliver [21, 22] whose algorithm constructs the graphs top down, by doing a hill climbing search through the ....

William J. Masek. A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Massachusetts Institute of Technology, 1976.

No context found.

W. Masek, A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.

No context found.

W. Masek. A fast algorithm for the string editing problem and decision graph complexity. M.Sc. Thesis, Massachusetts Institute of Technology, Cambridge, May 1976.

No context found.

Masek, W.: A fast algorithm for the string editing problem and decision graph complexity. M. Sc. Thesis, MIT (1976)

No context found.

W. Masek, A fast algorithm for the string editing problem and decision graph complexity. Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1976.

No context found.

W. Masek, A Fast Algorithm for the String Editing Problem and Decision Graph Complexity, M.Sc. Thesis, Massachusetts Institute of Technology, Cambridge, May 1976.

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