Computing with Noise - Phase Transitions in Boolean Formulas
نویسندگان
چکیده
Computing circuits composed of noisy logical gates and their ability to represent arbitrary boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.
منابع مشابه
Noisy random Boolean formulae: a statistical physics perspective.
Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates...
متن کاملO ct 1 99 7 Phase transitions in the generalization behaviour of multilayer perceptrons : II . The influence of noise ∗
We extend our study of phase transitions in the generalization behaviour of multilayer perceptrons with non-overlapping receptive fields to the problem of the influence of noise concerning e.g. the input units and/or the couplings between the input units and the hidden units of the second layer (='input noise') or the final output unit (='output noise'). Without output noise, the output itself ...
متن کاملPhase transitions and memory effects in the dynamics of Boolean networks
Abstract The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system’s quenched disorder and are sampled from a given distribution. The framework accommodates a v...
متن کاملSatisfiability Algorithms and Lower Bounds for Boolean Formulas over Finite Bases
We give a #SAT algorithm for boolean formulas over arbitrary finite bases. Let Bk be the basis composed of all boolean functions on at most k inputs. For Bk-formulas on n inputs of size cn, our algorithm runs in time 2n(1−δc,k) for δc,k = c −O(c2k2k). We also show the average-case hardness of computing affine extractors using linear-size Bk-formulas. We also give improved algorithms and lower b...
متن کاملN ov 2 00 3 Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances
This paper analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, this paper proves that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review letters
دوره 103 24 شماره
صفحات -
تاریخ انتشار 2009