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Extending CL-reducibility on array noncomputable degrees
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-28 DOI: 10.1016/j.ic.2024.105258
Nan Fang , Wolfgang Merkle
{"title":"Extending CL-reducibility on array noncomputable degrees","authors":"Nan Fang ,&nbsp;Wolfgang Merkle","doi":"10.1016/j.ic.2024.105258","DOIUrl":"10.1016/j.ic.2024.105258","url":null,"abstract":"<div><div>Given a function <em>f</em>, <em>f</em>-bounded-Turing (<em>f</em>-bT-) reducibility is the Turing reducibility with use function bounded by <em>f</em>. In the special case where <span><math><mi>f</mi><mo>=</mo><mrow><mi>id</mi></mrow><mo>+</mo><mi>c</mi></math></span> (with id being the identity function and <em>c</em> a constant), this is referred to as cl-reducibility. In a work by Barmpalias, Fang, and Lewis-Pye, it was proven that there exist two left-c.e. reals such that no left-c.e. real <span><math><mo>(</mo><mrow><mi>id</mi></mrow><mo>+</mo><mi>g</mi><mo>)</mo></math></span>-bT-computes both of them whenever <em>g</em> is computable, nondecreasing, and satisfies <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mi>g</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>=</mo><mo>∞</mo></math></span>. Moreover, such maximal pairs exist precisely within every array noncomputable degree. This result generalizes a prior result on cl-reducibility, which states that there exist two left-c.e. reals such that no left-c.e. real cl-computes both of them. An open question remained as to whether a similar extension could apply to another result on cl-reducibility, which asserts that there exists a left-c.e. real not cl-reducible to any random left-c.e. real. We answer this question affirmatively, providing a simpler proof compared to previous works. Additionally, we streamline the proof of the initial extension.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105258"},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100143","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}
引用次数: 0
Probabilistic judgment aggregation with conditional independence constraints
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-28 DOI: 10.1016/j.ic.2024.105256
Magdalena Ivanovska , Marija Slavkovik
{"title":"Probabilistic judgment aggregation with conditional independence constraints","authors":"Magdalena Ivanovska ,&nbsp;Marija Slavkovik","doi":"10.1016/j.ic.2024.105256","DOIUrl":"10.1016/j.ic.2024.105256","url":null,"abstract":"<div><div>Probabilistic judgment aggregation is concerned with aggregating judgments about probabilities of logically related issues. It takes as input imprecise probabilistic judgments over the issues given by a group of agents and defines rules of aggregating the individual judgments into a collective opinion representative for the group. The process of aggregation can be subject to constraints, i.e., aggregation rules can be required to satisfy certain properties. We explore how probabilistic independence constraints can be represented and incorporated into the aggregation process.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105256"},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100142","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}
引用次数: 0
ltlf synthesis under environment specifications for reachability and safety properties
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-28 DOI: 10.1016/j.ic.2024.105255
Benjamin Aminof , Giuseppe De Giacomo , Antonio Di Stasio , Hugo Francon , Sasha Rubin , Shufang Zhu
{"title":"ltlf synthesis under environment specifications for reachability and safety properties","authors":"Benjamin Aminof ,&nbsp;Giuseppe De Giacomo ,&nbsp;Antonio Di Stasio ,&nbsp;Hugo Francon ,&nbsp;Sasha Rubin ,&nbsp;Shufang Zhu","doi":"10.1016/j.ic.2024.105255","DOIUrl":"10.1016/j.ic.2024.105255","url":null,"abstract":"<div><div>In this paper, we study <span>ltl</span><sub><em>f</em></sub> synthesis under environment specifications for arbitrary reachability and safety properties. We consider both kinds of properties for both agent tasks and environment specifications, providing a complete landscape of synthesis algorithms. For each case, we devise a specific algorithm (optimal wrt complexity of the problem) and prove its correctness. The algorithms combine common building blocks in different ways. While some cases are already studied in literature others are studied here for the first time.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105255"},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143100144","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}
引用次数: 0
Distributed fractional local ratio and independent set approximation 分布式分数局部比率和独立集近似值
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-22 DOI: 10.1016/j.ic.2024.105238
Magnús M. Halldórsson , Dror Rawitz
{"title":"Distributed fractional local ratio and independent set approximation","authors":"Magnús M. Halldórsson ,&nbsp;Dror Rawitz","doi":"10.1016/j.ic.2024.105238","DOIUrl":"10.1016/j.ic.2024.105238","url":null,"abstract":"<div><div>We consider the <span>Maximum Weight Independent Set</span> problem, with a focus on obtaining good approximations for graphs of small maximum degree Δ. We give deterministic local algorithms running in time <span><math><mi>poly</mi><mo>(</mo><mi>Δ</mi><mo>,</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below <span><math><mfrac><mrow><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and a further improvement to <span><math><mn>8</mn><mo>/</mo><mn>5</mn><mo>+</mo><mi>ε</mi></math></span> when <span><math><mi>Δ</mi><mo>=</mo><mn>3</mn></math></span>.</div><div>Technically, this is achieved by leveraging the <em>fractional local ratio</em> technique, for a first application in a distributed setting.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105238"},"PeriodicalIF":0.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723840","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}
引用次数: 0
A parallel algorithm for counting parse trees 解析树计数并行算法
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-19 DOI: 10.1016/j.ic.2024.105237
Margarita Mikhelson, Alexander Okhotin
{"title":"A parallel algorithm for counting parse trees","authors":"Margarita Mikhelson,&nbsp;Alexander Okhotin","doi":"10.1016/j.ic.2024.105237","DOIUrl":"10.1016/j.ic.2024.105237","url":null,"abstract":"<div><div>A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic circuit of depth at most <span><math><mn>6</mn><msup><mrow><mo>(</mo><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> and with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></math></span> elements, where the constant factors in the big-O notation depend on the grammar. Then, the circuit is improved using fast matrix multiplication to use only <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>5.38</mn></mrow></msup><mo>)</mo></math></span> elements, while preserving depth <span><math><mi>O</mi><mo>(</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"303 ","pages":"Article 105237"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723839","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}
引用次数: 0
Asymptotically optimal synthesis of reversible circuits 可逆电路的渐进优化合成
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-08 DOI: 10.1016/j.ic.2024.105235
Xian Wu, Lvzhou Li
{"title":"Asymptotically optimal synthesis of reversible circuits","authors":"Xian Wu,&nbsp;Lvzhou Li","doi":"10.1016/j.ic.2024.105235","DOIUrl":"10.1016/j.ic.2024.105235","url":null,"abstract":"<div><div>Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> for the synthesis of <em>n</em>-wire reversible circuits was proved. Whether this lower bound has a matching upper bound was listed as one of the future challenging open problems in the survey (Saeedi and Markov (2013) <span><span>[1]</span></span>). In this paper we propose an algorithm to implement an arbitrary <em>n</em>-wire reversible circuit with no more than <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> elementary gates, and thus close the open problem.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105235"},"PeriodicalIF":0.8,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655748","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}
引用次数: 0
Non-linear communication via graded modal session types 通过分级模式会话类型进行非线性交流
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-11-04 DOI: 10.1016/j.ic.2024.105234
Danielle Marshall , Dominic Orchard
{"title":"Non-linear communication via graded modal session types","authors":"Danielle Marshall ,&nbsp;Dominic Orchard","doi":"10.1016/j.ic.2024.105234","DOIUrl":"10.1016/j.ic.2024.105234","url":null,"abstract":"<div><div>Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, strict linearity is limiting since there exist useful communication patterns that rely on non-linear behaviours. For example, shared channels can repeatedly spawn a process with binary communication along a fresh linear channel. Non-linearity can be introduced in a controlled way through the concept of <em>graded modal types</em>, which are a framework encompassing various kinds of <em>coeffect</em> (describing how computations make demands on their context). This paper shows how graded modalities can work alongside session types, enabling various non-linear concurrency behaviours to be re-introduced precisely. The ideas are demonstrated using Granule, a functional language with linear, indexed, and graded modal types. We define a core calculus capturing the requisite features and our new graded primitives, then present an operational model and establish various key properties.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105234"},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655749","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}
引用次数: 0
Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms 定点方程系统：抽象、博弈、向上技术和局部算法
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-24 DOI: 10.1016/j.ic.2024.105233
Paolo Baldan , Barbara König , Tommaso Padoan
{"title":"Systems of fixpoint equations: Abstraction, games, up-to techniques and local algorithms","authors":"Paolo Baldan ,&nbsp;Barbara König ,&nbsp;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}
引用次数: 0
Unifying lower bounds for algebraic machines, semantically 代数机器的统一下界，语义上
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-21 DOI: 10.1016/j.ic.2024.105232
Thomas Seiller , Luc Pellissier , Ulysse Léchine
{"title":"Unifying lower bounds for algebraic machines, semantically","authors":"Thomas Seiller ,&nbsp;Luc Pellissier ,&nbsp;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}
引用次数: 0
Introducing variables in the evolution rules of P systems 在 P 系统的进化规则中引入变量
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-10-16 DOI: 10.1016/j.ic.2024.105231
Bogdan Aman
{"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}
引用次数: 0
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