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Coherent control and distinguishability of quantum channels via PBS-diagrams 基于pbs图的量子信道的相干控制和可分辨性
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-03-02 DOI: 10.4230/LIPIcs.MFCS.2021.22
C. Branciard, A. Cl'ement, M. Mhalla, S. Perdrix
{"title":"Coherent control and distinguishability of quantum channels via PBS-diagrams","authors":"C. Branciard, A. Cl'ement, M. Mhalla, S. Perdrix","doi":"10.4230/LIPIcs.MFCS.2021.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.22","url":null,"abstract":"We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). As standard completely positive trace preserving maps are known not to be appropriate to represent coherently controlled quantum channels, we propose to instead use purified channels, an extension of Stinespring's dilation. We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117179462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Simplest Non-Regular Deterministic Context-Free Language 最简单的非规则确定性上下文无关语言
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-02-20 DOI: 10.4230/LIPIcs.MFCS.2021.63
P. Jančar, Jirí Síma
{"title":"Simplest Non-Regular Deterministic Context-Free Language","authors":"P. Jančar, Jirí Síma","doi":"10.4230/LIPIcs.MFCS.2021.63","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.63","url":null,"abstract":"We introduce a new notion of C-simple problems for a class C of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is C-simple if it can be reduced to each problem in C. This can be viewed as a conceptual counterpart to C-hard problems to which all problems in C reduce. Our concrete example is the class of non-regular deterministic context-free languages (DCFL′), with a truth-table reduction by Mealy machines. The main technical result is a proof that the DCFL′ language L# = {01 | n ≥ 1} is DCFL′-simple, and can be thus viewed as one of the simplest languages in the class DCFL′, in a precise sense. The notion of DCFL′-simple languages is nontrivial: e.g., the language LR = {wcw | w ∈ {a, b}∗} is not DCFL′-simple. By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that C-simple problems under suitable reductions can provide a tool for expanding the lower-bound results known for single problems to the whole classes of problems. 2012 ACM Subject Classification Theory of computation → Grammars and context-free languages; Theory of computation → Problems, reductions and completeness; Theory of computation → Transducers","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125586605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Keyboards as a New Model of Computation 键盘作为一种新的计算模式
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-02-19 DOI: 10.4230/LIPIcs.MFCS.2021.49
Yoan G'eran, Bastien Laboureix, Corto Mascle, Valentin D. Richard
{"title":"Keyboards as a New Model of Computation","authors":"Yoan G'eran, Bastien Laboureix, Corto Mascle, Valentin D. Richard","doi":"10.4230/LIPIcs.MFCS.2021.49","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.49","url":null,"abstract":"We introduce a new formalisation of language computation, called keyboards. We consider a set of atomic operations (writing a letter, erasing a letter, going to the right or to the left) and we define a keyboard as a set of finite sequences of such operations, called keys. The generated language is the set of words obtained by applying some non-empty sequence of those keys. Unlike classical models of computation, every key can be applied anytime. We define various classes of languages based on different sets of atomic operations, and compare their expressive powers. We also compare them to rational, context-free and context-sensitive languages. We obtain a strict hierarchy of classes, whose expressiveness is orthogonal to the one of the aforementioned classical models. We also study closure properties of those classes, as well as fundamental complexity problems on keyboards. 2012 ACM Subject Classification Theory of computation","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115164818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Synthesizing Computable Skolem Functions for First Order Logic 一阶逻辑中可计算Skolem函数的合成
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-02-15 DOI: 10.4230/LIPIcs.MFCS.2022.30
S. Akshay, Supratik Chakraborty
{"title":"On Synthesizing Computable Skolem Functions for First Order Logic","authors":"S. Akshay, Supratik Chakraborty","doi":"10.4230/LIPIcs.MFCS.2022.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.30","url":null,"abstract":"Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such Skolem constants and/or functions admit effectively computable interpretations. Indeed, the question of whether there exists an effectively computable interpretation of a Skolem function, and if so, how to automatically synthesize it, is fundamental to their use in several applications, such as planning, strategy synthesis, program synthesis etc. In this paper, we investigate the computability of Skolem functions and their automated synthesis in the full generality of first order logic. We first show a strong negative result, that even under mild assumptions on the vocabulary, it is impossible to obtain computable interpretations of Skolem functions. We then show a positive result, providing a precise characterization of first-order theories that admit effective interpretations of Skolem functions, and also present algorithms to automatically synthesize such interpretations. We discuss applications of our characterization as well as complexity bounds for Skolem functions (interpreted as Turing machines).","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124005292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Universal gauge-invariant cellular automata 通用尺度不变元胞自动机
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-02-13 DOI: 10.4230/LIPIcs.MFCS.2021.9
P. Arrighi, Marin Costes, Nathanael Eon
{"title":"Universal gauge-invariant cellular automata","authors":"P. Arrighi, Marin Costes, Nathanael Eon","doi":"10.4230/LIPIcs.MFCS.2021.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.9","url":null,"abstract":"Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then extends the theory so as make the global symmetry into a local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this process, known as gauge extension, within the Computer Science framework of Cellular Automata (CA). We prove that the CA which admit a relative gauge extension are exactly the globally symmetric ones (a.k.a the colour-blind). We prove that any CA admits a non-relative gauge extension. Both constructions yield universal gauge-invariant CA, but the latter allows for a first example where the gauge extension mediates interactions within the initial CA.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"287 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134255426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Generic Strategy Improvement Method for Simple Stochastic Games 简单随机对策的一般策略改进方法
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-02-09 DOI: 10.4230/LIPIcs.MFCS.2021.12
D. Auger, X. B. D. Montjoye, Y. Strozecki
{"title":"A Generic Strategy Improvement Method for Simple Stochastic Games","authors":"D. Auger, X. B. D. Montjoye, Y. Strozecki","doi":"10.4230/LIPIcs.MFCS.2021.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.12","url":null,"abstract":"We present a generic strategy iteration algorithm (GSIA) to find an optimal strategy of a simple stochastic game (SSG). We prove the correctness of GSIA, and derive a general complexity bound, which implies and improves on the results of several articles. First, we remove the assumption that the SSG is stopping, which is usually obtained by a polynomial blowup of the game. Second, we prove a tight bound on the denominator of the values associated to a strategy, and use it to prove that all strategy iteration algorithms are in fact fixed parameter tractable in the number of random vertices. All known strategy iteration algorithms can be seen as instances of GSIA, which allows to analyze the complexity of converge from below by Condon and to propose a class of algorithms generalising Gimbert and Horn's algorithm. These algorithms require less than $r!$ iterations in general and less iterations than the current best deterministic algorithm for binary SSGs given by Ibsen-Jensen and Miltersen.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125954294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Query-Competitive Sorting with Uncertainty 具有不确定性的查询竞争排序
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-12-17 DOI: 10.4230/LIPIcs.MFCS.2019.7
M. Halldórsson, M. S. D. Lima
{"title":"Query-Competitive Sorting with Uncertainty","authors":"M. Halldórsson, M. S. D. Lima","doi":"10.4230/LIPIcs.MFCS.2019.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2019.7","url":null,"abstract":"We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2 + O(1/k) if the components obtained have size at least k; (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also show that the advice complexity of the adaptive problem is floor[n/2] if no error threshold is allowed, and ceil[n/3 * lg 3] for the general case.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128256888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Maximum Cut on Interval Graphs of Interval Count Four Is NP-Complete 区间计数4的区间图上的最大割是np完全的
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-12-17 DOI: 10.4230/LIPIcs.MFCS.2021.38
C. M. Figueiredo, A. A. D. Melo, F. S. Oliveira, Ana Silva
{"title":"Maximum Cut on Interval Graphs of Interval Count Four Is NP-Complete","authors":"C. M. Figueiredo, A. A. D. Melo, F. S. Oliveira, Ana Silva","doi":"10.4230/LIPIcs.MFCS.2021.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.38","url":null,"abstract":"The computational complexity of the MaxCut problem restricted to interval graphs has been open since the 80's, being one of the problems proposed by Johnson on his Ongoing Guide to NP-completeness, and has been settled as NP-complete only recently by Adhikary, Bose, Mukherjee and Roy. On the other hand, many flawed proofs of polynomiality for MaxCut on the more restrictive class of unit/proper interval graphs (or graphs with interval count 1) have been presented along the years, and the classification of the problem is still unknown. In this paper, we present the first NP-completeness proof for MaxCut when restricted to interval graphs with bounded interval count, namely graphs with interval count 4.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124589136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A Linear-Time Nominal μ-Calculus with Name Allocation 具有名称分配的线性时间标称μ微积分
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-10-21 DOI: 10.4230/LIPIcs.MFCS.2021.58
D. Hausmann, Stefan Milius, Lutz Schröder
{"title":"A Linear-Time Nominal μ-Calculus with Name Allocation","authors":"D. Hausmann, Stefan Milius, Lutz Schröder","doi":"10.4230/LIPIcs.MFCS.2021.58","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.58","url":null,"abstract":"Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as nondetermininistic orbit-finite automata (NOFAs), where names play the role of data. Reasoning problems in such formalisms tend to be computationally hard. Name-binding nominal automata models such as regular nondeterministic nominal automata (RNNAs) have been shown to be computationally more tractable. In the present paper, we introduce a linear-time fixpoint logic Bar-muTL for finite words over an infinite alphabet, which features full negation and freeze quantification via name binding. We show by a nontrivial reduction to extended regular nondeterministic nominal automata that even though Bar-muTL allows unrestricted nondeterminism and unboundedly many registers, model checking Bar-muTL over RNNAs and satisfiability checking both have elementary complexity. For example, model checking is in 2ExpSpace, more precisely in parametrized ExpSpace, effectively with the number of registers as the parameter.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"558 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133661224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Abstract Congruence Criteria for Weak Bisimilarity 摘要弱双相似的同余准则
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-10-15 DOI: 10.4230/LIPIcs.MFCS.2021.88
Stelios Tsampas, Christian Williams, Dominique Devriese, F. Piessens
{"title":"Abstract Congruence Criteria for Weak Bisimilarity","authors":"Stelios Tsampas, Christian Williams, Dominique Devriese, F. Piessens","doi":"10.4230/LIPIcs.MFCS.2021.88","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.88","url":null,"abstract":"We introduce three general compositionality criteria over operational semantics that guarantee weak bisimulation being a congruence. Our work is founded upon Turi and Plotkin's mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. We demonstrate each criterion with various examples of success and failure and give a formal proof of correctness for our main result.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114072483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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