International Symposium on Mathematical Foundations of Computer Science最新文献_第4页

Sample compression schemes for balls in graphs 图中球的压缩方案示例

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-06-27 DOI: 10.48550/arXiv.2206.13254

Jérémie Chalopin, V. Chepoi, Fionn Mc Inerney, Sébastien Ratel, Y. Vaxès

引用次数: 3

Higher-order causal theories are models of BV-logic 高阶因果理论是bv逻辑的模型

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-05-23 DOI: 10.48550/arXiv.2205.11219

William D. Simmons, A. Kissinger

{"title":"Higher-order causal theories are models of BV-logic","authors":"William D. Simmons, A. Kissinger","doi":"10.48550/arXiv.2205.11219","DOIUrl":"https://doi.org/10.48550/arXiv.2205.11219","url":null,"abstract":"The Caus[ − ] construction takes a compact closed category of basic processes and yields a *-autonomous category of higher-order processes obeying certain signalling/causality constraints, as dictated by the type system in the resulting category. This paper looks at instances where the base category C satisfies additional properties yielding an affine-linear structure on Caus[ C ] and a substantially richer internal logic. While the original construction only gave multiplicative linear logic, here we additionally obtain additives and a non-commutative, self-dual sequential product yielding a model of Guglielmi’s BV logic. Furthermore, we obtain a natural interpretation for the sequential product as “A can signal to B, but not vice-versa”, which sits as expected between the non-signalling tensor and the fully-signalling (i.e. unconstrained) par. Fixing matrices of positive numbers for C recovers the BV category structure of probabilistic coherence spaces identified by Blute, Panangaden, and Slavnov, restricted to normalised maps. On the other hand, fixing the category of completely positive maps gives an entirely new model of BV consisting of higher order quantum channels, encompassing recent work in the study of quantum and indefinite causal structures.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129389928","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: 8

On Upward-Planar L-Drawings of Graphs 论图的向上平面l图

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-05-11 DOI: 10.48550/arXiv.2205.05627

Patrizio Angelini, S. Chaplick, Sabine Cornelsen, G. D. Lozzo

{"title":"On Upward-Planar L-Drawings of Graphs","authors":"Patrizio Angelini, S. Chaplick, Sabine Cornelsen, G. D. Lozzo","doi":"10.48550/arXiv.2205.05627","DOIUrl":"https://doi.org/10.48550/arXiv.2205.05627","url":null,"abstract":"In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge e is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail of e and of a horizontal segment ending at the head of e . Distinct edges may overlap, but not cross. Recently, upward-planar L-drawings have been studied for st -graphs, i.e., planar DAGs with a single source s and a single sink t containing an edge directed from s to t . It is known that a plane st-graph , i.e., an embedded st -graph in which the edge ( s, t ) is incident to the outer face, admits an upward-planar L-drawing if and only if it admits a bitonic st-ordering, which can be tested in linear time. We study upward-planar L-drawings of DAGs that are not necessarily st-graphs. On the combinatorial side, we show that a plane DAG admits an upward-planar L-drawing if and only if it is a subgraph of a plane st-graph admitting a bitonic st-ordering. This allows us to show that not every tree with a ﬁxed bimodal embedding admits an upward-planar L-drawing. Moreover, we prove that any acyclic cactus with a single source (or a single sink) admits an upward-planar L-drawing, which respects a given outerplanar embedding if there are no transitive edges. On the algorithmic side, we consider DAGs with a single source (or a single sink). We give linear-time testing algorithms for these DAGs in two cases: (i) when the drawing must respect a prescribed embedding and (ii) when no restriction is given on the embedding, but it is biconnected and series-parallel.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125802561","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

Enumeration Classes Defined by Circuits 电路定义的枚举类

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-05-01 DOI: 10.48550/arXiv.2205.00539

N. Creignou, Arnaud Durand, H. Vollmer

引用次数: 0

Skolem Meets Schanuel

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-28 DOI: 10.48550/arXiv.2204.13417

Y. Bilu, F. Luca, Joris Nieuwveld, J. Ouaknine, David Purser, J. Worrell

{"title":"Skolem Meets Schanuel","authors":"Y. Bilu, F. Luca, Joris Nieuwveld, J. Ouaknine, David Purser, J. Worrell","doi":"10.48550/arXiv.2204.13417","DOIUrl":"https://doi.org/10.48550/arXiv.2204.13417","url":null,"abstract":"The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a linear recurrence sequence is the union of a finite set and finitely many arithmetic progressions. The corresponding computational question, the Skolem Problem, asks to determine whether a given linear recurrence sequence has a zero term. Although the Skolem-Mahler-Lech Theorem is almost 90 years old, decidability of the Skolem Problem remains open. The main contribution of this paper is an algorithm to solve the Skolem Problem for simple linear recurrence sequences (those with simple characteristic roots). Whenever the algorithm terminates, it produces a stand-alone certificate that its output is correct -- a set of zeros together with a collection of witnesses that no further zeros exist. We give a proof that the algorithm always terminates assuming two classical number-theoretic conjectures: the Skolem Conjecture (also known as the Exponential Local-Global Principle) and the $p$-adic Schanuel Conjecture. Preliminary experiments with an implementation of this algorithm within the tool textsc{Skolem} point to the practical applicability of this method.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"400 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116027463","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

Polynomial Time Algorithm for ARRIVAL on Tree-like Multigraphs 树状多图到达的多项式时间算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-27 DOI: 10.48550/arXiv.2204.13151

D. Auger, Pierre Coucheney, Loric Duhaze

{"title":"Polynomial Time Algorithm for ARRIVAL on Tree-like Multigraphs","authors":"D. Auger, Pierre Coucheney, Loric Duhaze","doi":"10.48550/arXiv.2204.13151","DOIUrl":"https://doi.org/10.48550/arXiv.2204.13151","url":null,"abstract":"A rotor walk in a directed graph can be thought of as a deterministic version of a Markov Chain, where a pebble moves from vertex to vertex following a simple rule until a terminal vertex, or sink, is reached. The ARRIVAL problem, as defined by Dohrau and al., consists in determining which sink will be reached. While the walk itself can take an exponential number of steps, this problem belongs to the complexity class NP$cap$co-NP without being known to be in P. Several variants have been studied where we add one or two players to the model, defining deterministic analogs of stochastic models (e.g., Markovian decision processes, Stochastic Games) with rotor-routing rules instead of random transitions. The corresponding decision problem address the existence of strategies for players that ensure some condition on the reached sink. These problems are known to be $NP$-complete for one player and $PSPACE$-complete for two players. In this work, we define a class of directed graphs, namely tree-like multigraphs, which are multigraphs having the global shape of an undirected tree. We prove that the different variants of the reachability problem with zero, one, or two players can be solved in linear time, while the number of steps of rotor walks can still be exponential. To achieve this, we define a notion of return flow, which counts the number of times the pebble will bounce back in subtrees of the graph.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126053880","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

The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems 可对角线性动力系统的伪可达性问题

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-26 DOI: 10.48550/arXiv.2204.12253

Julian D'Costa, T. Karimov, J. Ouaknine, Mahmoud Salamati, S. Soudjani, J. Worrell

引用次数: 4

Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions 奇素维稳定器片段的完全zx演算

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-26 DOI: 10.4230/LIPIcs.MFCS.2022.24

Robert I. Booth, T. Carette

引用次数: 11

LOv-Calculus: A Graphical Language for Linear Optical Quantum Circuits 线性光学量子电路的图形语言

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-25 DOI: 10.4230/LIPIcs.MFCS.2022.35

A. Cl'ement, Nicolas Heurtel, Shane Mansfield, S. Perdrix, B. Valiron

引用次数: 12

Continuous rational functions are deterministic regular 连续有理函数是确定性正则函数

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-04-24 DOI: 10.48550/arXiv.2204.11235

Olivier Carton, Gaetan Dou'eneau-Tabot

引用次数: 1