arXiv - CS - Symbolic Computation最新文献_第5页

clauseSMT: A NLSAT-Based Clause-Level Framework for Satisfiability Modulo Nonlinear Real Arithmetic Theory clauseSMT: 基于 NLSAT 的可满足性模态非线性实数算术理论的条款级框架

arXiv - CS - Symbolic Computation Pub Date : 2024-06-04 DOI: arxiv-2406.02122

Zhonghan Wang

{"title":"clauseSMT: A NLSAT-Based Clause-Level Framework for Satisfiability Modulo Nonlinear Real Arithmetic Theory","authors":"Zhonghan Wang","doi":"arxiv-2406.02122","DOIUrl":"https://doi.org/arxiv-2406.02122","url":null,"abstract":"Model-constructing satisfiability calculus (MCSAT) framework has been applied\u0000to SMT problems on different arithmetic theories. NLSAT, an implementation\u0000using cylindrical algebraic decomposition for explanation, is especially\u0000competitive among nonlinear real arithmetic constraints. However, current\u0000Conflict-Driven Clause Learning (CDCL)-style algorithms only consider literal\u0000information for decision, and thus ignore clause-level influence on arithmetic\u0000variables. As a consequence, NLSAT encounters unnecessary conflicts caused by\u0000improper literal decisions. In this work, we analyze the literal decision caused conflicts, and introduce\u0000clause-level information with a direct effect on arithmetic variables. Two main\u0000algorithm improvements are presented: clause-level feasible-set based\u0000look-ahead mechanism and arithmetic propagation based branching heuristic. We\u0000implement our solver named clauseSMT on our dynamic variable ordering\u0000framework. Experiments show that clauseSMT is competitive on nonlinear real\u0000arithmetic theory against existing SMT solvers (cvc5, Z3, Yices2), and\u0000outperforms all these solvers on satisfiable instances of SMT(QF_NRA) in\u0000SMT-LIB. The effectiveness of our proposed methods are also studied.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252324","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

Representing Piecewise-Linear Functions by Functions with Minimal Arity 用具有最小 Arity 的函数表示片线性函数

arXiv - CS - Symbolic Computation Pub Date : 2024-06-04 DOI: arxiv-2406.02421

Christoph Koutschan, Anton Ponomarchuk, Josef Schicho

引用次数: 0

Polynomial Bounds of CFLOBDDs against BDDs CFLOBDD 针对 BDD 的多项式边界

arXiv - CS - Symbolic Computation Pub Date : 2024-06-03 DOI: arxiv-2406.01525

Xusheng ZhiUniversity of Wisconsin-Madison and Peking University, Thomas RepsUniversity of Wisconsin-Madison

{"title":"Polynomial Bounds of CFLOBDDs against BDDs","authors":"Xusheng ZhiUniversity of Wisconsin-Madison and Peking University, Thomas RepsUniversity of Wisconsin-Madison","doi":"arxiv-2406.01525","DOIUrl":"https://doi.org/arxiv-2406.01525","url":null,"abstract":"Binary Decision Diagrams (BDDs) are widely used for the representation of\u0000Boolean functions. Context-Free-Language Ordered Decision Diagrams (CFLOBDDs)\u0000are a plug-compatible replacement for BDDs -- roughly, they are BDDs augmented\u0000with a certain form of procedure call. A natural question to ask is, ``For a\u0000given Boolean function $f$, what is the relationship between the size of a BDD\u0000for $f$ and the size of a CFLOBDD for $f$?'' Sistla et al. established that, in\u0000the best case, the CFLOBDD for a function $f$ can be exponentially smaller than\u0000any BDD for $f$ (regardless of what variable ordering is used in the BDD);\u0000however, they did not give a worst-case bound -- i.e., they left open the\u0000question, ``Is there a family of functions ${ f_i }$ for which the size of a\u0000CFLOBDD for $f_i$ must be substantially larger than a BDD for $f_i$?'' For\u0000instance, it could be that there is a family of functions for which the BDDs\u0000are exponentially more succinct than any corresponding CFLOBDDs. This paper studies such questions, and answers the second question posed\u0000above in the negative. In particular, we show that by using the same variable\u0000ordering in the CFLOBDD that is used in the BDD, the size of a CFLOBDD for any\u0000function $f$ cannot be far worse than the size of the BDD for $f$. The bound\u0000that relates their sizes is polynomial: If BDD $B$ for function $f$ is of size\u0000$|B|$ and uses variable ordering $textit{Ord}$, then the size of the CFLOBDD\u0000$C$ for $f$ that also uses $textit{Ord}$ is bounded by $O(|B|^3)$. The paper also shows that the bound is tight: there is a family of functions\u0000for which $|C|$ grows as $Omega(|B|^3)$.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252119","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

A Synergistic Approach In Network Intrusion Detection By Neurosymbolic AI 利用神经符号人工智能进行网络入侵检测的协同方法

arXiv - CS - Symbolic Computation Pub Date : 2024-06-03 DOI: arxiv-2406.00938

Alice Bizzarri, Chung-En Yu, Brian Jalaian, Fabrizio Riguzzi, Nathaniel D. Bastian

{"title":"A Synergistic Approach In Network Intrusion Detection By Neurosymbolic AI","authors":"Alice Bizzarri, Chung-En Yu, Brian Jalaian, Fabrizio Riguzzi, Nathaniel D. Bastian","doi":"arxiv-2406.00938","DOIUrl":"https://doi.org/arxiv-2406.00938","url":null,"abstract":"The prevailing approaches in Network Intrusion Detection Systems (NIDS) are\u0000often hampered by issues such as high resource consumption, significant\u0000computational demands, and poor interpretability. Furthermore, these systems\u0000generally struggle to identify novel, rapidly changing cyber threats. This\u0000paper delves into the potential of incorporating Neurosymbolic Artificial\u0000Intelligence (NSAI) into NIDS, combining deep learning's data-driven strengths\u0000with symbolic AI's logical reasoning to tackle the dynamic challenges in\u0000cybersecurity, which also includes detailed NSAI techniques introduction for\u0000cyber professionals to explore the potential strengths of NSAI in NIDS. The\u0000inclusion of NSAI in NIDS marks potential advancements in both the detection\u0000and interpretation of intricate network threats, benefiting from the robust\u0000pattern recognition of neural networks and the interpretive prowess of symbolic\u0000reasoning. By analyzing network traffic data types and machine learning\u0000architectures, we illustrate NSAI's distinctive capability to offer more\u0000profound insights into network behavior, thereby improving both detection\u0000performance and the adaptability of the system. This merging of technologies\u0000not only enhances the functionality of traditional NIDS but also sets the stage\u0000for future developments in building more resilient, interpretable, and dynamic\u0000defense mechanisms against advanced cyber threats. The continued progress in\u0000this area is poised to transform NIDS into a system that is both responsive to\u0000known threats and anticipatory of emerging, unseen ones.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252118","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

Shape Constraints in Symbolic Regression using Penalized Least Squares 使用惩罚性最小二乘法的符号回归中的形状约束

arXiv - CS - Symbolic Computation Pub Date : 2024-05-31 DOI: arxiv-2405.20800

Viktor Martinek, Julia Reuter, Ophelia Frotscher, Sanaz Mostaghim, Markus Richter, Roland Herzog

{"title":"Shape Constraints in Symbolic Regression using Penalized Least Squares","authors":"Viktor Martinek, Julia Reuter, Ophelia Frotscher, Sanaz Mostaghim, Markus Richter, Roland Herzog","doi":"arxiv-2405.20800","DOIUrl":"https://doi.org/arxiv-2405.20800","url":null,"abstract":"We study the addition of shape constraints and their consideration during the\u0000parameter estimation step of symbolic regression (SR). Shape constraints serve\u0000as a means to introduce prior knowledge about the shape of the otherwise\u0000unknown model function into SR. Unlike previous works that have explored shape\u0000constraints in SR, we propose minimizing shape constraint violations during\u0000parameter estimation using gradient-based numerical optimization. We test three algorithm variants to evaluate their performance in identifying\u0000three symbolic expressions from a synthetically generated data set. This paper\u0000examines two benchmark scenarios: one with varying noise levels and another\u0000with reduced amounts of training data. The results indicate that incorporating\u0000shape constraints into the expression search is particularly beneficial when\u0000data is scarce. Compared to using shape constraints only in the selection\u0000process, our approach of minimizing violations during parameter estimation\u0000shows a statistically significant benefit in some of our test cases, without\u0000being significantly worse in any instance.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252120","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

Practical Modelling with Bigraphs 使用 Bigraphs 建立实用模型

arXiv - CS - Symbolic Computation Pub Date : 2024-05-31 DOI: arxiv-2405.20745

Blair Archibald, Muffy Calder, Michele Sevegnani

引用次数: 0

ParSEL: Parameterized Shape Editing with Language ParSEL：用语言进行参数化形状编辑

arXiv - CS - Symbolic Computation Pub Date : 2024-05-30 DOI: arxiv-2405.20319

Aditya Ganeshan, Ryan Y. Huang, Xianghao Xu, R. Kenny Jones, Daniel Ritchie

{"title":"ParSEL: Parameterized Shape Editing with Language","authors":"Aditya Ganeshan, Ryan Y. Huang, Xianghao Xu, R. Kenny Jones, Daniel Ritchie","doi":"arxiv-2405.20319","DOIUrl":"https://doi.org/arxiv-2405.20319","url":null,"abstract":"The ability to edit 3D assets from natural language presents a compelling\u0000paradigm to aid in the democratization of 3D content creation. However, while\u0000natural language is often effective at communicating general intent, it is\u0000poorly suited for specifying precise manipulation. To address this gap, we\u0000introduce ParSEL, a system that enables controllable editing of high-quality 3D\u0000assets from natural language. Given a segmented 3D mesh and an editing request,\u0000ParSEL produces a parameterized editing program. Adjusting the program\u0000parameters allows users to explore shape variations with a precise control over\u0000the magnitudes of edits. To infer editing programs which align with an input\u0000edit request, we leverage the abilities of large-language models (LLMs).\u0000However, while we find that LLMs excel at identifying initial edit operations,\u0000they often fail to infer complete editing programs, and produce outputs that\u0000violate shape semantics. To overcome this issue, we introduce Analytical Edit\u0000Propagation (AEP), an algorithm which extends a seed edit with additional\u0000operations until a complete editing program has been formed. Unlike prior\u0000methods, AEP searches for analytical editing operations compatible with a range\u0000of possible user edits through the integration of computer algebra systems for\u0000geometric analysis. Experimentally we demonstrate ParSEL's effectiveness in\u0000enabling controllable editing of 3D objects through natural language requests\u0000over alternative system designs.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"149 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192393","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 the Problem of Separating Variables in Multivariate Polynomial Ideals 论多元多项式理想中的变量分离问题

arXiv - CS - Symbolic Computation Pub Date : 2024-05-29 DOI: arxiv-2405.19223

Manfred Buchacher, Manuel Kauers

引用次数: 0

Unit-Aware Genetic Programming for the Development of Empirical Equations 用于开发经验公式的单元感知遗传编程

arXiv - CS - Symbolic Computation Pub Date : 2024-05-29 DOI: arxiv-2405.18896

Julia Reuter, Viktor Martinek, Roland Herzog, Sanaz Mostaghim

{"title":"Unit-Aware Genetic Programming for the Development of Empirical Equations","authors":"Julia Reuter, Viktor Martinek, Roland Herzog, Sanaz Mostaghim","doi":"arxiv-2405.18896","DOIUrl":"https://doi.org/arxiv-2405.18896","url":null,"abstract":"When developing empirical equations, domain experts require these to be\u0000accurate and adhere to physical laws. Often, constants with unknown units need\u0000to be discovered alongside the equations. Traditional unit-aware genetic\u0000programming (GP) approaches cannot be used when unknown constants with\u0000undetermined units are included. This paper presents a method for dimensional\u0000analysis that propagates unknown units as ''jokers'' and returns the magnitude\u0000of unit violations. We propose three methods, namely evolutive culling, a\u0000repair mechanism, and a multi-objective approach, to integrate the dimensional\u0000analysis in the GP algorithm. Experiments on datasets with ground truth\u0000demonstrate comparable performance of evolutive culling and the multi-objective\u0000approach to a baseline without dimensional analysis. Extensive analysis of the\u0000results on datasets without ground truth reveals that the unit-aware algorithms\u0000make only low sacrifices in accuracy, while producing unit-adherent solutions.\u0000Overall, we presented a promising novel approach for developing unit-adherent\u0000empirical equations.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192454","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

Learning from Uncertain Data: From Possible Worlds to Possible Models 从不确定性数据中学习：从可能的世界到可能的模型

arXiv - CS - Symbolic Computation Pub Date : 2024-05-28 DOI: arxiv-2405.18549

Jiongli Zhu, Su Feng, Boris Glavic, Babak Salimi

引用次数: 0