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Process Logic (PL) is a language for reasoning about the behavior of a program during a computation, while Propositional Dynamic Logic (PDL) can only reason about the input-output states of a program. Nevertheless, we show that to each PL model M there corresponds in a natural way a PDL, model Mt such that every path in M is represented by a state in Mt. Moreover, to every PL formula p there corresponds...
Several results in Algorithmic Information Theory establish upper bounds on the difference between descriptional complexity and the logarithm of "apriori probability". It was conjectured that these two quantities coincide to within an additive constant. Here, we disprove this conjecture and show that the known overall upper bound on the difference is exact. The proof uses a memory-allocation...
We examine the class of matrices that satisfy Commoner's sufficient condition for total unimodularity [C], which we call restricted totally unimodular (RTUM). We show that a matrix is RTUM if and only if it can be decomposed in a very simple way into the incidence matrices (or their transposes) of bipartite graphs or directed graphs, and give a linear time algorithm to perform this task. Based on...
Let SPS(f(n)) denote the solvable path system problem for path systems of bandwidth f(n) and SPS (f(n)) the corresponding problem for monotone systems. Let DTISP (poly, f(n)) denote the polynomial time and simultaneous f(n) space class and SC = UkDTISP (poly, logkn). Let ASPACE (f(n)) denote the sets accepted by f(n) space bounded alternating TMs and ASPACE (f(n)) the corresponding one-way TM family...
We show an Ω(n/log n) lower bound on the total number of operations necessary to compute 0-1 polynomials of degree n in the model with complex preconditioning. The best previous result was Ω(n1/2/log n). This yields the first asymptotically optimal lower bound on the complexity of 0-1 polynomials in this model. We show also that there are 0-1 polynomials of degree n that require Ω(n1/2/log n) additive...
Fully polynomial approximation algorithms for knapsack problems are presented. These algorithms are based on ideas of Ibarra and Kim, with modifications which yield better time and space bounds, and also tend to improve the practicality of the procedures. Among the principal improvements are the introduction of a more efficient method of scaling and the use of a median-finding routine to eliminate...
In this paper Valiant's decision procedure for equivalence of deterministic finite-turn pushdown machines is improved upon. The improved equivalence test is: Given two mahcines, one constructs a pushdown machine that simulates them simultaneously and accepts a string iff it is accepted by exactly one of them. The given machines are equivalent iff the simulating pda accepts the empty language. The...
At the heart of a number of arithmetic complexity problems are some basic questions in tensor analysis. Questions regarding the complexity of multiplication operations which are n-linear are most easily studied in a tensor analytic framework. Certain results of tensor analysis are used in this paper to provide insight into the solution of some of these problems. Methods are given to determine a partial...
Fault detecting test sets to detect multiple stuck-at-faults in certain networks realizing Reed-Muller canonic expressions are given. It is shown that to detect t faults, t ≥ 1, in a network realizing an arbitrary n-variable logic function only 4 + Σ i=1 [log22t] (in) tests need be applied ([x] is the integer part of x) and that these tests are independent of the function being realized. Techniques...
A physico-mathematical basis is used to establish bounds TD(n) on the time needed to compute n-argument functions by spatially distributed primitive devices or composite systems D. The axioms used concern the speed, packing density and noise threshold of the energy with which any computing device detects or alters the physical representation of information. The principal result is that TD(n) grows...
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