181,712 research outputs found
Logic on words
First published in the Bulletin of the European Association of Theoretical Computer Science 54 (1994), 145-165.This dialog between Quisani, Yuri Gurevich's imaginary student, and the author, was published in the "Logic in Computer Science Column" of the EATCS Bulletin. It is first addressed to logicians. This dialog is an occasion to present the connections between Büchi's sequential calculus and the theory of finite automata. In particular, the essential role of first order formulæ is emphasized. The quantifier hierarchies on these formulæ are an occasion to present open problems
The umbilical cord of finite model theory
Model theory was born and developed as a part of mathematical logic. It has
various application domains but is not beholden to any of them. A priori, the
research area known as finite model theory would be just a part of model theory
but didn't turn out that way. There is one application domain -- relational
database management -- that finite model theory had been beholden to during a
substantial early period when databases provided the motivation and were the
main application target for finite model theory.
Arguably, finite model theory was motivated even more by complexity theory.
But the subject of this paper is how relational database theory influenced
finite model theory.
This is NOT a scholarly history of the subject with proper credits to all
participants. My original intent was to cover just the developments that I
witnessed or participated in. The need to make the story coherent forced me to
cover some additional developments.Comment: To be published in the Logic in Computer Science column of the
February 2023 issue of the Bulletin of the European Association for
Theoretical Computer Scienc
Automata Column: The Complexity of Reachability in Vector Addition Systems
International audienceThe program of the 30th Symposium on Logic in Computer Science held in 2015 in Kyoto included two contributions on the computational complexity of the reachability problem for vector addition systems: Blondin, Finkel, Göller, Haase, and McKenzie [2015] attacked the problem by providing the first tight complexity bounds in the case of dimension 2 systems with states, while Leroux and Schmitz [2015] proved the first complexity upper bound in the general case. The purpose of this column is to present the main ideas behind these two results, and more generally survey the current state of affairs
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
Stochastic assembly of sublithographic nanoscale interfaces
We describe a technique for addressing individual nanoscale wires with microscale control wires without using lithographic-scale processing to define nanoscale dimensions. Such a scheme is necessary to exploit sublithographic nanoscale storage and computational devices. Our technique uses modulation doping to address individual nanowires and self-assembly to organize them into nanoscale-pitch decoder arrays. We show that if coded nanowires are chosen at random from a sufficiently large population, we can ensure that a large fraction of the selected nanowires have unique addresses. For example, we show that N lines can be uniquely addressed over 99% of the time using no more than /spl lceil/2.2log/sub 2/(N)/spl rceil/+11 address wires. We further show a hybrid decoder scheme that only needs to address N=O(W/sub litho-pitch//W/sub nano-pitch/) wires at a time through this stochastic scheme; as a result, the number of unique codes required for the nanowires does not grow with decoder size. We give an O(N/sup 2/) procedure to discover the addresses which are present. We also demonstrate schemes that tolerate the misalignment of nanowires which can occur during the self-assembly process
Nonphotolithographic nanoscale memory density prospects
Technologies are now emerging to construct molecular-scale electronic wires and switches using bottom-up self-assembly. This opens the possibility of constructing nanoscale circuits and memories where active devices are just a few nanometers square and wire pitches may be on the order of ten nanometers. The features can be defined at this scale without using photolithography. The available assembly techniques have relatively high defect rates compared to conventional lithographic integrated circuits and can only produce very regular structures. Nonetheless, with proper memory organization, it is reasonable to expect these technologies to provide memory densities in excess of 10/sup 11/ b/cm/sup 2/ with modest active power requirements under 0.6 W/Tb/s for random read operations
Evolving more efficient digital circuits by allowing circuit layout evolution and multi-objective fitness
We use evolutionary search to design combinational logic circuits. The technique is based on evolving the functionality and connectivity of a rectangular array of logic cells whose dimension is defined by the circuit layout.
The main idea of this approach is to improve quality of the circuits evolved by the GA by reducing the number of active gates used. We accomplish this by combining two ideas: 1) using multi-objective fitness function; 2) evolving circuit layout. It will be shown that using these two approaches allows us to increase the quality of evolved circuits.
The circuits are evolved in two phases. Initially the genome fitness in given by the percentage of output bits that are correct. Once 100% functional circuits have been evolved, the number of gates actually used in the circuit is taken into account in the fitness function. This allows us to evolve circuits with 100% functionality and minimise the number of active gates in circuit structure. The population is initialised with heterogeneous circuit layouts and the circuit layout is allowed to vary during the evolutionary process. Evolving the circuit layout together with the function is one of the distinctive features of proposed approach. The experimental results show that allowing the circuit layout to be flexible is useful when we want to evolve circuits with the smallest number of gates used. We find that it is better to use a fixed circuit layout when the objective is to achieve the highest number of 100% functional circuits. The two-fitness strategy is most effective when we allow a large number of generations
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