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Circuit complexity and the expressive power of generalized first-order formulas [chapter]

Howard Straubing
1992 Lecture Notes in Computer Science  
The circuit complexity classes AC 0 ; ACC; and CC (also called pure-ACC) can be characterized as the classes of languages de nable in certain extensions of rst-order logic.  ...  logical formulas to be either unary relations, or the order relation < :  ...  First-order variables are interpreted as positions in the string, and the rst-order predicate symbols are interpreted as either purely numerical relations on the positions, or as asserting that a certain  ... 
doi:10.1007/3-540-55719-9_60 fatcat:7fvf2ebkzffbjivfw3g2htytpy

Extension of the leeson formula to phase noise calculation in transistor oscillators with complex tanks

J. Nallatamby, M. Prigent, M. Camiade, J.J. Obregon
2003 IEEE transactions on microwave theory and techniques  
We have derived the right coefficient in terms of the energy stored and power dissipated in the circuit.  ...  A comparison with nonlinear simulations of the phase noise in oscillator circuits with complex feedback tanks demonstrates the validity of the new expression.  ...  GENERAL EXPRESSION OF THE GROUP DELAY AS A FUNCTION OF THE ENERGY STORED AND POWER DISSIPATED IN A ONE-PORT LINEAR CIRCUIT For comparison purposes with the passive circuit -factor, the general expression  ... 
doi:10.1109/tmtt.2003.808670 fatcat:oedgj7e7dbhx3mmzlx6ifrxsya

Division Is In Uniform TC0 [chapter]

William Hesse
2001 Lecture Notes in Computer Science  
A key step of our proof is the discovery of a first-order formula expressing exponentiation modulo any number of polynomial size.  ...  This has been perhaps the outstanding natural problem known to be in a standard circuit complexity class, but not known to be in its uniform version. We show that indeed division is in uniform TC 0 .  ...  We work within the framework of descriptive complexity, and show that there is a first-order formula using majority quantifiers that expresses division.  ... 
doi:10.1007/3-540-48224-5_9 fatcat:vu6dhiadb5drjduq47va4sfobq

On the Complexity of Some Problems on Groups Input as Multiplication Tables

David Mix Barrington, Peter Kadau, Klaus-Jörn Lange, Pierre McKenzie
2001 Journal of computer and system sciences (Print)  
Finally, we examine the implications of our results for the complexity of iterated multiplication, powering, and division of integers in the context of the recent results of Chiu, Davida, and Litow and  ...  cyclicity and nilpotency can each be tested in FOLL 5 L.  ...  Some of these, and much other fruitful work on this project, occurred at a Dagstuhl seminar in November 1999 attended by three of the authors.  ... 
doi:10.1006/jcss.2001.1764 fatcat:7sicpde6rzf7heo3s5gvnksywu

On uniformity within NC1

David A. Mix Barrington, Neil Immerman, Howard Straubing
1990 Journal of computer and system sciences (Print)  
Two such conditions, stricter than NC' uniformity, have appeared in recent research: Immerman's families of circuits defined by first-order formulas and a uniformity corresponding to Buss' deterministic  ...  Here we give characterizations of subclasses of the regular languages based on their logical expressibility, extending recent work of Straubing, Thtrien, and Thomas.  ...  In addition we would like to thank the two anonymous referees for their comments, which have greatly improved the presentation.  ... 
doi:10.1016/0022-0000(90)90022-d fatcat:zdlwqu25tnh6rbht7wd264jfe4

The generalization of A. E. Kennelly theory of complex representation of the electrical quantities in sinusoidal periodic regime to the one and three-phase electric quantities in non-sinusoidal periodic regime [article]

Gheorghe Mihai
2010 arXiv   pre-print
In this paper, a new mathematical method of electrical circuits calculus is proposed based on the theory of the complex linear operators in matrix form.  ...  The newly proposed method generalizes the theory of complex representation of electrical quantities in sinusoidal periodic regime to the non-sinusoidal periodic regime.  ...  In order to also be used in non-sinusoidal periodic regime, it is first used the superposition principle through which, each harmonica takes action in the electrical circuit.  ... 
arXiv:1002.2645v1 fatcat:qvtarmvkgvhxhn6thq6oa3lavm

Capacitor-value calculation in a three-phase electronic circuit with the help of complex numbers

Zsófia Németh
2022 Mesterséges intelligencia  
In order to find this angle, it is not enough to find the expression for the current in one circuit, I have to find in both of them and then add them up (I6).  ...  As I expressed above, only the complex forms are suitable for addition, so now I will try to convert I1 and I2 to their complex forms by finding the true power and the reactive power using the Pythagorean  ... 
doi:10.35406/mi.2022.1.9 fatcat:cbvhzjxlk5fwbjzawwlow6skua

Circuits, Logic and Games (Dagstuhl Seminar 15401)

Mikolaj Bojanczyk, Meena Mahajan, Thomas Schwentick, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
complexity and circuit lower bounds inherently using methods from logic and algebra Proof systems with low circuit complexity Dynamic complexity: understanding the dynamic expressive power of small depth  ...  Over the years, there has been a lot of interplay between circuit complexity and logic.  ...  Sreejith: Non-definability of Languages by Generalized First-order Formulas over (N, +).  ... 
doi:10.4230/dagrep.5.9.105 dblp:journals/dagstuhl-reports/BojanczykMSV15 fatcat:pv6oxt7lnvhkbczugwxmvumdxq

Analysis and future trend of short-circuit power

K. Nose, T. Sakurai
2000 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
This paper also handles the short-circuit power of series-connected MOSFET structures which appear in NAND and other complex gates.  ...  A closed-form expression for short-circuit power dissipation of CMOS gates is presented which takes short-channel effects into consideration.  ...  average of the two quantities to build the general formula, , which covers both of the slow and fast input case.  ... 
doi:10.1109/43.863642 fatcat:iu55te7bejbc3fs5eknrx542sm

The Kolmogorov expressive power of Boolean query languages

Jerzy Tyszkiewicz
1998 Theoretical Computer Science  
In order to answer it we develop a Kolmogorov complexity based measure of expressive power of Boolean query languages over finite structures.  ...  We explore some connections between the proposed Kohnogorov expressive power of Boolean queries in these languages and their standard expressive power, in particular with the definability of order.  ...  I wish to thank Andrzej Tarlecki, who asked me the question if the restricted Kolmogorov expressive power had anything to do with optimization of queries.  ... 
doi:10.1016/s0304-3975(97)00094-7 fatcat:qoeogljv5ndi3cpczctgy5o2t4

Queries with arithmetical constraints

Stéphane Grumbach, Jianwen Su
1997 Theoretical Computer Science  
In this paper, we study the expressive power and the complexity of first-order logic with arithmetic, as a query language over relational and constraint databases.  ...  We then tackle the problem of the expressive power, with the definability of the parity and the connectivity, which are the most classical examples of queries not expressible in first-order logic over  ...  The increase of the number of relations and arithmetic functions in a first-order language generally results in an increase of its expressive power.  ... 
doi:10.1016/s0304-3975(96)00194-6 fatcat:2l24uv556reahd6xv2u57wxgqu

Computability of the additive complexity of algebraic circuits with root extracting

Dima Grigoriev, Marek Karpinski
1996 Theoretical Computer Science  
It is the first computability result of this sort on the additive complexity of algebraic circuits.  ...  We design an algorithm for computing the generalized (i.e. for algebraic circuits with root extracting, cf. [9, 10, 131) additive complexity of any rational function.  ...  Acknowledgements We are thankful to Richard Cleve for starting us up to think about the additive complexity of polynomials, and to Allan Borodin, Joachim von zur Gathen, Thomas Lickteig, Michael Singer  ... 
doi:10.1016/0304-3975(95)00177-8 fatcat:k27q2vkxzvbdpcoay3c6bp4pve

Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)

Anuj Dawar, Erich Grädel, Phokion G. Kolaitis, Thomas Schwentick, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17361 "Finite and Algorithmic Model Theory".  ...  We formalize agent-based models as stochastic processes whose states are metafinite models, and we define a notion of abstraction.  ...  Our main results are conditions that imply an abstraction is sound, and further conditions that imply it preserves the Markov property.  ... 
doi:10.4230/dagrep.7.9.1 dblp:journals/dagstuhl-reports/DawarGKS17 fatcat:teyilwvdgrd6tch2gdb4d4dd5m


Federico Moro, Roberto Turri
2012 Progress in Electromagnetics Research B  
Original expressions are given for single circuit lines of any type of arrangement and double circuit lines in both super-bundle and low-reactance conductor phasing.  ...  The accuracy of approximate formulas is demonstrated by comparison with exact formulas for computing the rms field distribution.  ...  field intensities generated by each circuit independently, and θ pq can assume values 0, −2π/3, +2π/3, depending on the phase ordering of line currents.  ... 
doi:10.2528/pierb11112206 fatcat:jqwzukjp2zcale6cpyinwgrobu

Supporting Lists in a Data Model (A Timely Approach)

Joel E. Richardson
1992 Very Large Data Bases Conference  
This framework provides many opportunities for optimization and parallelism, and it lends insight to the meaning and complexity of a temporal formula.  ...  The extended algebra allows the expression of a significantly larger class of queries than previously possible.  ...  I would like to thank Bobbie Cochrane, Bill Cody, Laura Haas, Peter Schwarz, Moshe Vardi, Jennifer Widom, and the VLDB referees for helping to improve the quality of this paper.  ... 
dblp:conf/vldb/Richardson92 fatcat:exr6ut6ksfbq7oir4xavbvyxdm
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