{"title":"Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms","authors":"Paolo Baldan , Barbara König , Tommaso Padoan","doi":"10.1016/j.ic.2024.105233","DOIUrl":"10.1016/j.ic.2024.105233","url":null,"abstract":"<div><div>Systems of fixpoint equations over complete lattices, which combine least and greatest fixpoints, often arise from verification tasks such as model checking and behavioural equivalence checking. In this paper we develop a theory of approximation in the style of abstract interpretation, where a system over some concrete domain is abstracted into a system on a suitable abstract domain, ensuring sound and possibly complete over-approximations of the solutions. We also show how up-to techniques, commonly used to simplify coinductive proofs, fit into this framework, interpreted as abstractions. Additionally, we characterise the solution of fixpoint equation systems through parity games, extending prior work limited to continuous lattices. This game-based approach allows for local algorithms that verify system properties, such as determining whether a state satisfies a formula or two states are behaviourally equivalent. We describe a local algorithm, that can be combined with abstraction and up-to techniques to speed up the computation.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105233"},"PeriodicalIF":0.8,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unifying lower bounds for algebraic machines, semantically","authors":"Thomas Seiller , Luc Pellissier , Ulysse Léchine","doi":"10.1016/j.ic.2024.105232","DOIUrl":"10.1016/j.ic.2024.105232","url":null,"abstract":"<div><div>We present a new abstract method for proving lower bounds in computational complexity based on the notion of topological and measurable entropy for dynamical systems. It is shown to generalise several previous lower bounds results from the literature in algebraic complexity, thus providing a unifying framework for “topological” proofs of lower bounds. We further use this method to prove that <span>maxflow</span>, a <figure><img></figure> complete problem, is not computable in polylogarithmic time on parallel random access machines (<span>pram</span>s) working with real numbers. This improves on a result of Mulmuley since the class of machines considered extends the class “<span>pram</span>s without bit operations”, making more precise the relationship between Mulmuley's result and similar lower bounds on real <span>pram</span>s.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105232"},"PeriodicalIF":0.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introducing variables in the evolution rules of P systems","authors":"Bogdan Aman","doi":"10.1016/j.ic.2024.105231","DOIUrl":"10.1016/j.ic.2024.105231","url":null,"abstract":"<div><div>In membrane systems evolution rules are constructed using only objects from a finite alphabet. In this paper we investigate rules in which variables are used. Namely, we define Variable P systems in which the rules containing variables need to be instantiated at the start of each computational step with values from some predefined sets of sets of objects.</div><div>The modelling power of variable P systems is described by simulating some basic arithmetic operations over a (multi)set of positive numbers (addition, multiplication, or a combination of them). The main advantage of using variable P systems consists in the small number of used rules regardless how many numbers are involved in the operation: e.g., the addition requires only 3 rules, while the multiplication only 27 rules.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105231"},"PeriodicalIF":0.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Perspective on complexity measures targeting read-once branching programs","authors":"Yaqiao Li , Pierre McKenzie","doi":"10.1016/j.ic.2024.105230","DOIUrl":"10.1016/j.ic.2024.105230","url":null,"abstract":"<div><div>A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-<em>k</em> branching programs for the tree evaluation problem. Other computation problems are studied as well. In particular, a common view of a function studied by Gál and a function studied by Bollig and Wegener leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-<em>k</em> branching programs for the GEN function is also derived, independently from the new measures.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105230"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Different strokes in randomised strategies: Revisiting Kuhn's theorem under finite-memory assumptions","authors":"James C.A. Main , Mickael Randour","doi":"10.1016/j.ic.2024.105229","DOIUrl":"10.1016/j.ic.2024.105229","url":null,"abstract":"<div><div>Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis.</div><div>Optimal strategies may require randomisation when dealing with inherently probabilistic goals, balancing multiple objectives, or in contexts of partial information. There is no unique way to define randomised strategies. For instance, one can use so-called <em>mixed</em> strategies or <em>behavioural</em> ones. In the most general setting, these two classes do not share the same expressiveness. A seminal result in game theory — <em>Kuhn's theorem</em> — asserts their equivalence in games of perfect recall.</div><div>This result crucially relies on the possibility for strategies to use <em>infinite memory</em>, i.e., unlimited knowledge of all past observations. However, computer systems are finite in practice. Hence it is pertinent to restrict our attention to <em>finite-memory</em> strategies, defined as automata with outputs. Randomisation can be implemented in these in different ways: the <em>initialisation</em>, <em>outputs</em> or <em>transitions</em> can be randomised or deterministic respectively. Depending on which aspects are randomised, the expressiveness of the corresponding class of finite-memory strategies differs.</div><div>In this work, we study two-player concurrent stochastic games and provide a complete taxonomy of the classes of finite-memory strategies obtained by varying which of the three aforementioned components are randomised. Our taxonomy holds in games of perfect and imperfect information with perfect recall, and in games with more than two players. We also provide an adapted taxonomy for games with imperfect recall.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105229"},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Beatrice Amico, Carlo Combi, Romeo Rizzi, Pietro Sala
{"title":"Predictive mining of multi-temporal relations","authors":"Beatrice Amico, Carlo Combi, Romeo Rizzi, Pietro Sala","doi":"10.1016/j.ic.2024.105228","DOIUrl":"10.1016/j.ic.2024.105228","url":null,"abstract":"<div><div>In this paper, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework and on a multi-temporal relational model. Different features are proposed for the Observation Window (OW), where we observe predictive data, for the Waiting Window (WW), and for the Prediction Window (PW), where the predicted event occurs. We then consider the concept of approximation for such APFDs, introduce new error measures, and discuss different strategies for deriving APFDs. We discuss the quality, i.e., the informative content, of the derived AFDs by considering their entropy and information gain. Moreover, we outline the results in deriving APFDs focusing on the Acute Kidney Injury (AKI). We use real clinical data contained in the MIMIC III dataset related to patients from Intensive Care Units to show the applicability of our approach to real-world data.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105228"},"PeriodicalIF":0.8,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142422711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Blazing a trail via matrix multiplications: A faster algorithm for non-shortest induced paths","authors":"Yung-Chung Chiu, Hsueh-I Lu","doi":"10.1016/j.ic.2024.105227","DOIUrl":"10.1016/j.ic.2024.105227","url":null,"abstract":"<div><div>For vertices <em>u</em> and <em>v</em> of an <em>n</em>-vertex graph <em>G</em>, a <em>uv-trail</em> of <em>G</em> is an induced <em>uv</em>-path of <em>G</em> that is not a shortest <em>uv</em>-path of <em>G</em>. Berger, Seymour, and Spirkl [<em>Discrete Mathematics</em> 2021] gave the previously only known polynomial-time algorithm, running in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>18</mn></mrow></msup><mo>)</mo></math></span> time, to either output a <em>uv</em>-trail of <em>G</em> or ensure that <em>G</em> admits no <em>uv</em>-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> Boolean matrices, leading to a largely improved <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4.75</mn></mrow></msup><mo>)</mo></math></span>-time algorithm. Our result improves the previous <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>21</mn></mrow></msup><mo>)</mo></math></span>-time algorithm by Cook, Horsfield, Preissmann, Robin, Seymour, Sintiari, Trotignon, and Vušković [<em>Journal of Combinatorial Theory, Series B</em>, 2024] for recognizing graphs with all holes the same length, and reduces the running time to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>7.75</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105227"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Truthful and privacy-preserving generalized linear models","authors":"Yuan Qiu , Jinyan Liu , Di Wang","doi":"10.1016/j.ic.2024.105225","DOIUrl":"10.1016/j.ic.2024.105225","url":null,"abstract":"<div><p>This paper explores estimating Generalized Linear Models (GLMs) when agents are strategic and privacy-conscious. We aim to design mechanisms that encourage truthful reporting, protect privacy, and ensure outputs are close to the true parameters. Initially, we address models with sub-Gaussian covariates and heavy-tailed responses with finite fourth moments, proposing a novel private, closed-form estimator. Our mechanism features: (1) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>-joint differential privacy with high probability; (2) <span><math><mi>o</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></math></span>-approximate Bayes Nash equilibrium for <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>-fraction of agents; (3) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> error in parameter estimation; (4) individual rationality for <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> of agents; (5) <span><math><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> payment budget. We then extend our approach to linear regression with heavy-tailed data, using an <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-norm shrinkage operator to propose a similar estimator and payment scheme.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105225"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Logical equivalences, homomorphism indistinguishability, and forbidden minors","authors":"Tim Seppelt","doi":"10.1016/j.ic.2024.105224","DOIUrl":"10.1016/j.ic.2024.105224","url":null,"abstract":"<div><p>Two graphs <em>G</em> and <em>H</em> are <em>homomorphism indistinguishable</em> over a graph class <span><math><mi>F</mi></math></span> if for all graphs <span><math><mi>F</mi><mo>∈</mo><mi>F</mi></math></span> the number of homomorphisms from <em>F</em> to <em>G</em> is equal to the number of homomorphisms from <em>F</em> to <em>H</em>. Many graph isomorphism relaxations such as (quantum) isomorphism, spectral, and logical equivalences can be characterised as homomorphism indistinguishability relations over certain graph classes.</p><p>Abstracting from the wealth of such instances, we show in this paper that equivalences w.r.t. any <em>self-complementarity</em> logic admitting a characterisation as homomorphism indistinguishability relation can be characterised by homomorphism indistinguishability over a minor-closed graph class. Self-complementarity is a mild property satisfied by most well-studied logics.</p><p>Furthermore, we classify all graph classes which are in a sense finite and satisfy the maximality condition of being <em>homomorphism distinguishing closed</em>, i.e. adding any graph to the class strictly refines its homomorphism indistinguishability relation. Thereby, we answer various questions raised by Roberson (2022) on properties of the homomorphism distinguishing closure.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105224"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000890/pdfft?md5=8f37aee0808075f72c988f0ff4dd0e3d&pid=1-s2.0-S0890540124000890-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multivariate to bivariate reduction for noncommutative polynomial factorization","authors":"V. Arvind , Pushkar S. Joglekar","doi":"10.1016/j.ic.2024.105223","DOIUrl":"10.1016/j.ic.2024.105223","url":null,"abstract":"<div><p>Based on Bergman's theorem, we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely,</p><ul><li><span>1.</span><span><p>Given an <em>n</em>-variate noncommutative polynomial <span><math><mi>f</mi><mo>∈</mo><mi>F</mi><mo>〈</mo><mi>X</mi><mo>〉</mo></math></span> over a field <span><math><mi>F</mi></math></span> as an arithmetic circuit, computing a complete factorization of <em>f</em> into irreducible factors is deterministic polynomial-time reducible to factorization of a noncommutative bivariate polynomial <span><math><mi>g</mi><mo>∈</mo><mi>F</mi><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></math></span>; the reduction transforms <em>f</em> into a circuit for <em>g</em>, and given a complete factorization of <em>g</em>, the reduction recovers a complete factorization of <em>f</em> in polynomial time.</p><p>The reduction works both in the white-box and the black-box setting.</p></span></li><li><span>2.</span><span><p>We show over the field of rationals that bivariate linear matrix factorization problem for <span><math><mn>4</mn><mo>×</mo><mn>4</mn></math></span> matrices is at least as hard as factoring square-free integers and for <span><math><mn>3</mn><mo>×</mo><mn>3</mn></math></span> matrices it is in polynomial time.</p></span></li></ul></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105223"},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}