The Size of a Formula as a Measure of Complexity
نویسندگان
چکیده
We propose a refinement of the usual Ehrenfeucht-Fräıssé game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to measure not only quantifier rank but also lengths of conjunctions and disjunctions needed for expressing a given property. Our game is similar to the game in [1] and in [5]. The most common measure of complexity of a first order sentence is its quantifier rank, and the method of Ehrenfeucht-Fräıssé games can be successfully used to prove lower bound results for this measure of complexity. However, the number of non-equivalent first order formulas of quantifier rank n is an exponential tower of height n with a polynomial depending on the vocabulary on the top. Thus we are not very close to knowing the formula
منابع مشابه
An Algorithm to Compute the Complexity of a Static Production Planning (RESEARCH NOTE)
Complexity is one of the most important issues of any production planning. The increase in complexity of production planning can cause inconsistency between a production plan and an actual outcome. The complexity generally can be divided in two categories, the static complexity and the dynamic complexity, which can be computed using the ant ropy formula. The formula considers the probability of...
متن کاملMeasurement of Complexity and Comprehension of a Program Through a Cognitive Approach
The inherent complexity of the software systems creates problems in the software engineering industry. Numerous techniques have been designed to comprehend the fundamental characteristics of software systems. To understand the software, it is necessary to know about the complexity level of the source code. Cognitive informatics perform an important role for better understanding the complexity o...
متن کاملDetermination of the attenuation coefficient for megavoltage photons in the water phantom
Background: Attenuation coefficient (μ) plays an important role in calculations of treatment planning systems, as well as determination of dose distributions in external beam therapy, dosimetry, protection, phantom materials and industry. So, its exact measurement or calculation is very important. The aim of this study was to evaluate the μ in different points in the water phantom anal...
متن کاملA Novel Method for Detection of Epilepsy in Short and Noisy EEG Signals Using Ordinal Pattern Analysis
Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is...
متن کاملEFL Textbooks, L2 Contacts, and Teacher Self-Efficacy: Impact on Learners’ Development of Oral Complexity, Accuracy, and Fluency
Researchers have extensively compared different L2 learning contexts, such as EFL versus study-abroad, for their impacts on oral production; however, scant attention, if any, has been paid to comparing EFL settings in terms of input factors such as textbooks, amount of contacts in L2, and teachers. Accordingly, the effects of these factors on the oral production skills were investigated in this...
متن کاملThe Impact of Quranic Stories on Students’ Questioning Skills
The Impact of Quranic Stories on Students’ Questioning Skills A.R. Shahabadi Gh. Ahghar, Ph.D. S. Beheshti, Ph.D. The present study was carried out to examine the impact of Quranic stories on students’ questioning skills. The population of the study included high school male 2nd graders in district 5 of Tehran in academic year 2015-2016. The study was a quasi-ex...
متن کامل