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Equivalence and Conditional Independence in Atomic Sheaf logic 24

Equivalence and Conditional Independence in Atomic Sheaf Log...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Simpson, Alex Univ Ljubljana Fac Math & Phys Inst Math Phys & Mech Ljubljana Slovenia

ISBN: (纸本)9798400706608

We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that such relations can be modelled naturally in atomic sheaf toposes. Equivalence of variables is modelled by an intrinsic relation of atomic equivalence that is possessed by every atomic sheaf. We identify additional structure on the category generating the atomic topos (primarily, the existence of a system of independent pullbacks) that allows conditional independence to be interpreted in the topos. We then study the logic of equivalence and conditional independence that is induced by the internal logic of the topos. this atomic sheaf logic is a classical logic that validates a number of fundamental reasoning principles relating equivalence and conditional independence. As a concrete example of this abstract framework, we use the atomic topos over the category of surjections between finite nonempty sets as our main running example. In this category, the interpretations of equivalence and conditional independence coincide with those given by the multiteam semantics of independence logic, in which the role of equivalence is taken by the relation of mutual inclusion. A major difference from independence logic is that, in atomic sheaf logic, the multiteam semantics of the equivalence and conditional independence relations is embedded within a classical surrounding logic. At the end of the paper, we briefly outline two other instances of our framework, to demonstrate its versatility. the first of these is a category of probability sheaves, in which atomic equivalence is equality-in-distribution, and the conditional independence relation is the usual probabilistic one. Our other example is the Schanuel topos (equivalent to nominal sets) where equivalence is orbit equality and conditional independence amounts to a relative form of separatedne

关键词： logics for probability categorical probability theory conditional independence dependence logic team semantics sheaves toposes

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First order distinguishability of sparse random graphs 24

First order distinguishability of sparse random graphs

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Hershko, Tal Zhukovskii, Maksim CALTECH Pasadena CA 91125 USA Univ Sheffield Sheffield S Yorkshire England

ISBN: (纸本)9798400706608

We study the problem of distinguishing between two independent samples G(n)(1), G(n)(2) of a binomial random graph G(n, p) by first order (FO) sentences. Shelah and Spencer proved that, for a constant alpha is an element of(0, 1), G(n, n(-alpha)) obeys FO zero-one law if and only if alpha is irrational. therefore, for irrational alpha is an element of(0, 1), any fixed FO sentence does not distinguish between G(n)(1), G(n)(2) with asymptotical probability 1 (w.h.p.) as n ->infinity. We show that the minimum quantifier depth ka of a FO sentence G(n)(1), G(n)(2) = G(n)(1), G(n)(2)(G(n)(1), G(n)(2)) distinguishing between G(n)(1), G(n)(2) depends on how closely a can be approximated by rationals: for all non-Liouville alpha is an element of (0, 1), k(alpha) = Omega(ln ln lnn) w.h.p.;there are irrational alpha is an element of (0, 1) with ka that grow arbitrarily slowly w.h.p.;k(alpha) = Op ( ln n/ln ln n) for all alpha is an element of(0, 1). the main ingredients in our proofs are a novel randomized algorithm that generates asymmetric strictly balanced graphs as well as a new method to study symmetry groups of randomly perturbed graphs.

关键词： first order logic random graphs zero-one laws quantifier depth distinguishability of graphs graph isomorphism asymmetry of graphs Liouville numbers

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the Impact of Heterogeneous logic on Adders and Multipliers in VTR 34

The Impact of Heterogeneous Logic on Adders and Multipliers ...

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34th International Workshop on Rapid System Prototyping - Shortening the Path from Specification to Prototype

作者： Jafarof, Navid Kent, Kenneth B. Univ New Brunswick Fredericton NB Canada

ISBN: (纸本)9798400704109

this paper presents an extension of the Verilog-to-Routing (VTR) computer-Aided Design (CAD) tool, focusing specifically on the utilization of heterogeneous logic for both multipliers and adders. We build upon the heterogeneous logic implementation of adders in VTR by addressing bugs and refining the implementation. this research aims to uncover the optimal configuration in terms of critical path delay (CPD) and device area for hard and soft logic implementations within different architectures and designs. Our findings show that a balanced approach, instead of the exclusive utilization of either hard or soft logic, can yield superior results. Extensive testing reveals significant improvements in speed and potential reductions in device size. the results validate the implementation's success and suggest future directions for enhancing the use of different types of logic in VTR.

关键词： CAD FPGA VTR Hard logic Soft logic ODIN II Multiplier Adder Optimization Synthesis

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On the Decidability of Monadic Second-Order logic with Arithmetic Predicates 39

On the Decidability of Monadic Second-Order Logic with Arith...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Berthe, Valerie Karimov, Toghrul Nieuwveld, Joris Ouaknine, Joel Vahanwala, Mihir Worrell, James Univ Paris Cite IRIF CNRS Paris France Max Planck Inst Software Syst Saarbrucken Germany Univ Oxford Dept Comp Sci Oxford England

We investigate the decidability of the monadic second-order (MSO) theory of the structure , for various unary predicates P-1,...,....P-k subset of N. We focus in particular on 'arithmetic' predicates arising i... 详细信息

ISBN: (纸本)9798400706608

We investigate the decidability of the monadic second-order (MSO) theory of the structure < N;<, P-1,...,....P-k >, for various unary predicates P-1,...,....P-k subset of N. We focus in particular on 'arithmetic' predicates arising in the study of linear recurrence sequences, such as fixed-base powers Pow(k) = {k(n) : n is an element of N},. k-th powers N-k = {n(k) : n is an element of N}, and the set of terms of the Fibonacci sequence Fib = {0, 1, 2, 3, 5, 8, 13,...} (and similarly for other linear recurrence sequences having a single, non-repeated, dominant characteristic root). We obtain several new unconditional and conditional decidability results, a select sample of which are the following: . the MSO theory of < N;<, Pow(2), Fib > is decidable;. the MSO theory of < N;<, Pow(2), Pow(3), Pow(6)> is decidable;. the MSO theory of < N;<, Pow(2), Pow(3), Pow(5)> is decidable assuming Schanuel's conjecture;. the MSO theory of < N;<, Pow(4), N-2 > is decidable;. the MSO theory of < N;<, Pow(2), N-2 > is Turing-equivalent to the MSO theory of < N;<, S >, where S is the predicate corresponding to the binary expansion of root 2. (As the binary expansion of root 2 is widely believed to be normal, the corresponding MSO theory is in turn expected to be decidable.) these results are obtained by exploiting and combining techniques from dynamical systems, number theory, and automata theory. the full version of this paper can be found in [8].

关键词： Monadic second-order logic linear recurrence sequences toric words cutting sequences decidability

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Bounding the Weisfeiler-Leman Dimension via a Depth Analysis of I/R-Trees 24

Bounding the Weisfeiler-Leman Dimension via a Depth Analysis...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Kiefer, Sandra Neuen, Daniel Univ Oxford Oxford England Univ Regensburg Regensburg Germany

ISBN: (纸本)9798400706608

the Weisfeiler-Leman (WL) dimension is an established measure for the inherent descriptive complexity of graphs and relational structures. It corresponds to the number of variables that are needed and sufficient to define the object of interest in a counting version of first-order logic (FO). these bounded-variable counting logics were even candidates to capture graph isomorphism, until a celebrated construction due to Cai, Furer, and Immerman [Combinatorica 1992] showed that Omega(n) variables are required to distinguish all non-isomorphic n-vertex graphs. Still, very little is known about the precise number of variables required and sufficient to define every n-vertex graph. For the bounded-variable (non-counting) FO fragments, Pikhurko, Veith, and Verbitsky [Discret. Appl. Math. 2006] provided an upper bound of n+3/2 and showed that it is essentially tight. Our main result yields that, in the presence of counting quantifiers, n/4 +o(n) variables suffice. this shows that counting does allow us to save variables when defining graphs. As an application of our techniques, we also show new bounds in terms of the vertex cover number of the graph. To obtain the results, we introduce a new concept called the WL depth of a graph. We use it to analyze branching trees within the Individualization/Refinement (I/R) paradigm from the domain of isomorphism algorithms. We extend the recursive procedure from the I/R paradigm by the possibility of splitting the graphs into independent parts. then we bound the depth of the obtained branching trees, which translates into bounds on the WL dimension and thereby on the number of variables that suffice to define the graphs.

关键词： Weisfeiler-Leman algorithm first-order logic counting quantifiers individualization/refinement paradigm

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δis for Dialectica 24

δis for Dialectica

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39th annual acm/ieee symposium on logic in computer science, LICS 2024

作者： Kerjean, Marie Morgane Pédrot, Pierre-Marie Computer Science Cnrs Lipn Université Sorbonne Paris Nord Villetaneuse60009647 France Inria Nantes60013373 France

ISBN: (纸本)9798400706608

Automatic Differentiation is the study of the efficient computation of differentials. While the first automatic differentiation algorithms are concomitant with the birth of computer science, the specific backpropagation algorithm has been brought to a modern light by its application to neural networks. this work unveils a surprising connection between backpropagation and Gödel's Dialectica interpretation, a logical translation that realizes semi-classical axioms. this unexpected correspondence is exploited through different logical settings. In particular, we show that the computational interpretation of Dialectica translates to the differential λ-calculus and that Differential Linear logic subsumes the logical interpretation of Dialectica. © 2024 Copyright is held by the owner/author(s). Publication rights licensed to acm.

关键词： Differentiation (calculus)

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Incremental SAT-based Exact Synthesis 24

Incremental SAT-based Exact Synthesis

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34th Great Lakes symposium on VLSI (GLSVLSI)

作者： Zou, Sunan Zhang, Jiaxi Luo, Guojie Peking Univ Sch Comp Sci Beijing Peoples R China Peking Univ Ctr Energy Efficient Comp & Applicat Beijing Peoples R China

ISBN: (纸本)9798400706059

Exact synthesis is a critical technique in logic synthesis to generate optimal circuits for given Boolean functions. Recent progress in SAT solvers makes SAT-based methods practical. However, the intractable and unpredictable execution time has limited its application with potential quality degradation and runtime overhead. To ease such limitations, we propose an incremental SAT-based method for exact synthesis (IncSyn). It leverages previous knowledge to accelerate the finding of a new optimal circuit. IncSyn uncovers the relationships between functions and modifies the encoding and synthesis flow correspondingly. We speed up the exact synthesis by up to 15x and achieve scale advancements, solving considerable cases of up to 12-input Boolean functions within tolerable time. the proposed method reduces the average runtime for optimal library building and on-the-fly rewrite by 6% and 64%, respectively.

关键词： logic Synthesis Exact Synthesis SAT Problem Incremental Solving

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FFCL: Forward-Forward Net with Cortical Loops, Training and Inference on Edge Without Backpropogation 24

FFCL: Forward-Forward Net with Cortical Loops, Training and ...

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34th Great Lakes symposium on VLSI (GLSVLSI)

作者： Karkehabadi, Ali Homayoun, Houman Sasan, Avesta Univ Calif Davis Davis CA 95616 USA

ISBN: (纸本)9798400706059

the Forward-Forward Learning (FFL) algorithm is a recently proposed solution for training neural networks without needing memory-intensive backpropagation. During training, labels accompany input data, classifying them as positive or negative inputs. Each layer learns its response to these inputs independently. In this study, we enhance the FFL with the following contributions: 1) We optimize label processing by segregating label and feature forwarding between layers, enhancing learning performance. 2) By revising label integration, we enhance the inference process, reduce computational complexity, and improve performance. 3) We introduce feedback loops akin to cortical loops in the brain, where information cycles through and returns to earlier neurons, enabling layers to combine complex features from previous layers with lower-level features, enhancing learning efficiency.

关键词： logic Locking De-obfuscation Formal Verification

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On the complexity of Maslov's class K¯ 24

On the complexity of Maslov's class K¯

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39th annual acm/ieee symposium on logic in computer science, LICS 2024

作者： Fiuk, Oskar Kieronski, Emanuel Michielini, Vincent Institute of Computer Science University of Wroclaw Wroclaw60016147 Poland Faculty of Mathematics Informatics and Mechanics University of Warsaw Warsaw60013756 Poland

ISBN: (纸本)9798400706608

Maslov's class K is an expressive fragment of First-Order logic known to have decidable satisfiability problem, whose exact complexity, however, has not been established so far. We show that K has the exponential-sized model property, and hence its satisfiability problem is NExpTime-complete. Additionally, we get new complexity results on related fragments studied in the literature, and propose a new decidable extension of the uniform one-dimensional fragment (without equality). Our approach involves a use of satisfiability games tailored to K and a novel application of paradoxical tournament graphs. © 2024 Copyright is held by the owner/author(s). Publication rights licensed to acm.

关键词： Computability and decidability

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Ultra-Area-Efficient Cryogenic XNOR logic Gate with Superconducting Heater Cryotron to Advance High-Performance Computing 24

Ultra-Area-Efficient Cryogenic XNOR Logic Gate with Supercon...

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34th Great Lakes symposium on VLSI (GLSVLSI)

作者： Alam, Shamiul Aziz, Ahmedullah Univ Tennessee Knoxville TN 37916 USA

ISBN: (纸本)9798400706059

Superconducting electronics have garnered significant attention recently due to their exceptional speed and energy efficiency. they play a vital role in scaling quantum computers to thousands of qubits and offer unique advantages for high-performance computing and aerospace exploration. However, conventional Josephson junction-based superconducting circuits face scalability challenges due to flux trapping and struggle in driving high load impedances. To address these issues, three-terminal cryotron devices have emerged as a promising alternative. Here, we present a novel approach utilizing two heater cryotron devices to construct an XNOR gate, significantly enhancing the area efficiency of existing superconducting XNOR gates. XNOR logic plays a pivotal role in various applications including adder design, data center operations like copy verification and data encryption/decryption. Our designed XNOR logic gate boasts a substantial improvement in area efficiency compared to existing designs, requiring only two heater cryotron devices instead of the previous requirement of ten cryotron devices, leading to an 80% improvement in device count. this advancement holds promise for further optimizing superconducting circuitry for various applications.

关键词： Adder Cryogenic logic Heater Cryotron Superconducting XNOR

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