Third Advanced Course on Foundations of Computer Science

The Internet of Things designates a vision of an informationalized world, in which everyday objects are modified through computer technology such as RFID, sensors and sensor systems, tracking systems, or small computer units, giving them additional information or functions and integrating them with their environment. This paper explores the phenomenon of Internet of Things by applying some of the key concepts found in the philosophical works of Martin Heidegger and conducts a critical analysis using Martin Heidegger’s reflections on “world” and “technology” from Sein und Zeit (Being and Time) of 1957, and from the paper “Die Frage nach der Technik” (“The Question Concerning Technology”). The concept of “Ge-stell” introduced by Martin Heidegger to the philosophy of technology describes the situation of mankind and technology in a world shaped by modern technology. Both, mankind and technology, are tied to one dimension and share the same world. The world has been shaped and redesigned by technology, and the individual is completely tied into the technologized world. The basis for all Internet of Things concepts and installations is the expression of real-world things and processes as mathematical quantities and concepts, and the connecting of individual values and concepts with each other. The basis for all information technology is the reduction of reality to figures and calculable structures. Mathematics is the foundation of computer science, and thus the foundation of ubiquitous computing.

We consider two of the most fundamental theorems in cryptography. The first, due to Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364–1396] is that pseudorandom generators can be constructed from any one-way function. The second, due to Yao [Proceedings of the $23$rd Annual Symposium on Foundations of Computer Science (FOCS), 1982, pp. 80–91], states that the existence of weak one-way functions implies the existence of full-fledged one-way functions. These powerful plausibility results shape our understanding of hardness and randomness in cryptography, but unfortunately their proofs are not as tight (i.e., security preserving) as one may desire. This work revisits a technique that we call the randomized iterate, introduced by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163–1175]. This technique was used by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163–1175] to give a construction of pseudorandom generators from regular one-way functions. We simplify and strengthen this technique in order to obtain a similar construction, where the seed length of the resulting generators is as short as $\Theta(n \log n)$ (rather than $\Theta(n^3)$ achieved by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163–1175]). Our technique has the potential of implying seed length $\Theta(n)$, and the only bottleneck for such a result are the parameters of current generators against bounded-space computations. We give a construction with similar parameters for security amplification of regular one-way functions. This improves upon the construction of Goldreich et al. [Proceedings of the $31$st Annual Symposium on Foundations of Computer Science, (FOCS), 1990, pp. 318–326] in that the construction does not need to “know" the regularity parameter of the functions (in terms of security, the two reductions are incomparable). In addition, we use the randomized iterate to show a construction of a pseudorandom generator based on an exponentially hard one-way function that has a seed length of only $\Theta(n^2)$. This improves a recent result of Holenstein [Proceedings of the Theory of Cryptography, Third Theory of Cryptography Conference (TCC), 2006] that shows a construction with seed length $\Theta(n^5)$ based on such one-way functions. Finally, we show that the randomized iterate may even be useful in the general context of Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364–1396]. In particular, we use the randomized iterate to replace the basic building block of the Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364–1396] construction. Interestingly, this modification improves efficiency by an $\Theta(n^2)$ factor and reduces the seed length to $\Theta(n^7)$ (which also implies improvement in the security of the construction).

We consider a model of game-theoretic network design initially studied by Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004), where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004) proved that pure-strategy Nash equilibria always exist and that the price of stability—the ratio between the cost of the best Nash equilibrium and that of an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has a weight w i ≥1, and its cost share of an edge in its path equals w i times the edge cost, divided by the total weight of the players using the edge. This paper presents the first general results on weighted Shapley network design games. First, we give a simple example with no pure-strategy Nash equilibrium. This motivates considering the price of stability with respect to α-approximate Nash equilibria—outcomes from which no player can decrease its cost by more than an α multiplicative factor. Our first positive result is that O(log w max )-approximate Nash equilibria exist in all weighted Shapley network design games, where w max is the maximum player weight. More generally, we establish the following trade-off between the two objectives of good stability and low cost: for every α=Ω(log w max ), the price of stability with respect to O(α)-approximate Nash equilibria is O((log W)/α), where W is the sum of the players’ weights. In particular, there is always an O(log W)-approximate Nash equilibrium with cost within a constant factor of optimal. Finally, we show that this trade-off curve is nearly optimal: we construct a family of networks without o(log w max / log log w max )-approximate Nash equilibria, and show that for all α=Ω(log w max /log log w max ), achieving a price of stability of O(log W/α) requires relaxing equilibrium constraints by an Ω(α) factor.

48th Annual IEEE Symposium on Foundations of Computer Science - Title

For general antiferromagnetic 2-spin systems, including the hardcore model on weighted independent sets and the antiferromagnetic Ising model, there is an for the partition function on graphs of maximum degree when the infinite regular tree lies in the uniqueness region by Li, Lu, and Yin [Correlation Decay up to Uniqueness in Spin Systems, preprint, https://arxiv.org/abs/1111.7064, 2021]. Moreover, in the tree nonuniqueness region, Sly in [Computational transition at the uniqueness threshold, in Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science, 2010, pp. 287–296] showed that there is no to estimate the partition function unless . The algorithmic results follow from the correlation decay approach due to Weitz [Counting independent sets up to the tree threshold, in Proceedings of the 38th Annual ACM Symposium on Theory of Computing, 2006, pp. 140–149] or the polynomial interpolation approach developed by Barvinok [Combinatorics and Complexity of Partition Functions, Springer, 2016]. However, the running time is only polynomial for constant . For the hardcore model, recent work of Anari, Liu, and Oveis Gharan [Spectral independence in high-dimensional expanders and applications to the hardcore model, in Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science, 2020, pp. 1319–1330] establishes rapid mixing of the simple single-site Markov chain, known as the Glauber dynamics, in the tree uniqueness region. Our work simplifies their analysis of the Glauber dynamics by considering the total pairwise influence of a fixed vertex on other vertices, as opposed to the total influence of other vertices on , thereby extending their work to all 2-spin models and improving the mixing time. More important, our proof ties together the three disparate algorithmic approaches: we show that contraction of the so-called tree recursions with a suitable potential function, which is the primary technique for establishing efficiency of Weitz’s correlation decay approach and Barvinok’s polynomial interpolation approach, also establishes rapid mixing of the Glauber dynamics. We emphasize that this connection holds for all 2-spin models (both antiferromagnetic and ferromagnetic), and existing proofs for the correlation decay and polynomial interpolation approaches immediately imply rapid mixing of the Glauber dynamics. Our proof utilizes the fact that the graph partition function is a divisor of the partition function for Weitz’s self-avoiding walk tree. This fact leads to new tools for the analysis of the influence of vertices and may be of independent interest for the study of complex zeros.

We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis (2004) and Szegedy (2004). Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chains. In addition, it is conceptually simple and avoids some technical difficulties in the previous analyses of several algorithms based on quantum walk.

LOGIC – A foundation for computer science : V. Sperschneider and G. Antoniou, Addison-Wesley, Reading, MA, 1991. 495 pp., US$34.50, ISBN 0-201-56514-5.

Copyright and Reprint Permissions: Abstracting is permitted with credit to the source. Libraries may photocopy beyond the limits of US copyright law, for private use of patrons, those articles in this volume that carry a code at the bottom of the first page, provided that the per-copy fee indicated in the code is paid through the Copyright Clearance Center. The papers in this book comprise the proceedings of the meeting mentioned on the cover and title page. They reflect the authors' opinions and, in the interests of timely dissemination, are published as presented and without change. Their inclusion in this publication does not necessarily constitute endorsement by the editors or the Institute of Electrical and Electronics Engineers, Inc.

46th Annual IEEE Symposium on Foundations of Computer Science - Table of Contents

The 2-way quantum finite automaton introduced by Kondacs and Watrous [Proceedings of the 38th Annual Symposium on Foundations of Computer Science, 1997, IEEE Computer Society, pp. 66--75] can accept nonregular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1-way quantum finite automaton is reduced to a proper subset of the regular languages. In this paper we study two different models of 1-way quantum finite automata. The first model, termed measure-once quantum finite automata, was introduced by Moore and Crutchfield [ Theoret. Comput. Sci., 237 (2000), pp. 275--306], and the second model, termed measure-many quantum finite automata, was introduced by Kondacs and Watrous [Proceedings of the38th Annual Symposium on Foundations of Computer Science, 1997, IEEE Computer Society, pp. 66--75]. We characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group. We also show that it can be simulated by a probabilistic finite automaton and describe an algorithm that determines if two measure-once automata are equivalent. We prove several closure properties of the classes of languages accepted by measure-many automata, including inverse homomorphisms, and provide a new necessary condition for a language to be accepted by the measure-many model with bounded error. Finally, we show that piecewise testable sets can be accepted with bounded error by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.

We examine how to induce selfish heterogeneous users in a multicommodity network to reach an equilibrium that minimizes the social cost. In the absence of centralized coordination, we use the classical method of imposing appropriate taxes (tolls) on the edges of the network. We significantly generalize previous work (Yang and Huang in Transp. Res. Part B 38:1–15, [2004]; Karakostas and Kolliopoulos in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 268–276, [2004]; Fleischer et al. in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 277–285, [2004]) by allowing user demands to be elastic. In this setting the demand of a user is not fixed a priori but it is a function of the routing cost experienced, a most natural assumption in traffic and data networks.

46th Annual IEEE Symposium on Foundations of Computer Science - Title Page

formula omitted]-Regular languages are testable with a constant number of queries

Type theory is an elegant organisation of the fundamental principles of a foundational theory of computing, with theory taken in the sense of a scientific theory as well as a deductive theory. This theory generates a research programme. I examine the elements of this programme and assess progress. A large number of people world wide have been pursuing the type theory aspects of this research programme, so we can survey a large body of work created over a 20 year period for hints of success and failure and challenge. I first look at a few successes. Some of the applications we have attempted have not worked out as expected, and we don't know whether the fault lies with the type theory or elsewhere. I first describe a failure that is clearly not the type theory, but the state of the foundations of computational mathematics. Then we look at problems closer to the structure of modern type theories-problems suggested by the success of classical set theory.

We show that Nechiporuk's method [I. Wegener, The Complexity of Boolean Functions, Teubner-Wiley, New York, 1987] for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an $\Omega(n^2/\log^2 n)$ lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [A. Yao, Proceedings of 34th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1993, pp. 352--361] states that the majority function does not have a linear-size quantum formula. We also show that quantum formulas can be simulated by Boolean circuits of almost the same size.