arXiv - CS - Formal Languages and Automata Theory最新文献_第5页

Linear equations and recursively enumerable sets 线性方程和递推可数集

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-06-02 DOI: arxiv-2406.00688

Juha Honkala

引用次数: 0

The generating power of weighted tree automata with initial algebra semantics 具有初始代数语义的加权树自动机的生成能力

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-31 DOI: arxiv-2405.20753

Manfred Droste, Zoltán Fülöp, Andreja Tepavčević, Heiko Vogler

{"title":"The generating power of weighted tree automata with initial algebra semantics","authors":"Manfred Droste, Zoltán Fülöp, Andreja Tepavčević, Heiko Vogler","doi":"arxiv-2405.20753","DOIUrl":"https://doi.org/arxiv-2405.20753","url":null,"abstract":"We consider the images of the initial algebra semantics of weighted tree\u0000automata over strong bimonoids (hence also over semirings). These images are\u0000subsets of the carrier set of the underlying strong bimonoid. We consider\u0000locally finite, weakly locally finite, and bi-locally finite strong bimonoids.\u0000We show that there exists a strong bimonoid which is weakly locally finite and\u0000not locally finite. We also show that if the ranked alphabet contains a binary\u0000symbol, then for any finitely generated strong bimonoid, weighted tree automata\u0000can generate, via their initial algebra semantics, all elements of the strong\u0000bimonoid. As a consequence of these results, for weakly locally finite strong\u0000bimonoids which are not locally finite, weighted tree automata can generate\u0000infinite images provided that the input ranked alphabet contains at least one\u0000binary symbol. This is in sharp contrast to the setting of weighted string\u0000automata, where each such image is known to be finite. As a further\u0000consequence, for any finitely generated semiring, there exists a weighted tree\u0000automaton which generates, via its run semantics, all elements of the semiring.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255739","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

Reward Machines for Deep RL in Noisy and Uncertain Environments 噪声和不确定环境中的深度 RL 奖励机制

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-31 DOI: arxiv-2406.00120

Andrew C. Li, Zizhao Chen, Toryn Q. Klassen, Pashootan Vaezipoor, Rodrigo Toro Icarte, Sheila A. McIlraith

{"title":"Reward Machines for Deep RL in Noisy and Uncertain Environments","authors":"Andrew C. Li, Zizhao Chen, Toryn Q. Klassen, Pashootan Vaezipoor, Rodrigo Toro Icarte, Sheila A. McIlraith","doi":"arxiv-2406.00120","DOIUrl":"https://doi.org/arxiv-2406.00120","url":null,"abstract":"Reward Machines provide an automata-inspired structure for specifying\u0000instructions, safety constraints, and other temporally extended reward-worthy\u0000behaviour. By exposing complex reward function structure, they enable\u0000counterfactual learning updates that have resulted in impressive sample\u0000efficiency gains. While Reward Machines have been employed in both tabular and\u0000deep RL settings, they have typically relied on a ground-truth interpretation\u0000of the domain-specific vocabulary that form the building blocks of the reward\u0000function. Such ground-truth interpretations can be elusive in many real-world\u0000settings, due in part to partial observability or noisy sensing. In this paper,\u0000we explore the use of Reward Machines for Deep RL in noisy and uncertain\u0000environments. We characterize this problem as a POMDP and propose a suite of RL\u0000algorithms that leverage task structure under uncertain interpretation of\u0000domain-specific vocabulary. Theoretical analysis exposes pitfalls in naive\u0000approaches to this problem, while experimental results show that our algorithms\u0000successfully leverage task structure to improve performance under noisy\u0000interpretations of the vocabulary. Our results provide a general framework for\u0000exploiting Reward Machines in partially observable environments.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141255823","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

Oblivious Monitoring for Discrete-Time STL via Fully Homomorphic Encryption 通过完全同态加密实现离散时间 STL 的遗忘监控

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-27 DOI: arxiv-2405.16767

Masaki Waga, Kotaro Matsuoka, Takashi Suwa, Naoki Matsumoto, Ryotaro Banno, Song Bian, Kohei Suenaga

{"title":"Oblivious Monitoring for Discrete-Time STL via Fully Homomorphic Encryption","authors":"Masaki Waga, Kotaro Matsuoka, Takashi Suwa, Naoki Matsumoto, Ryotaro Banno, Song Bian, Kohei Suenaga","doi":"arxiv-2405.16767","DOIUrl":"https://doi.org/arxiv-2405.16767","url":null,"abstract":"When monitoring a cyber-physical system (CPS) from a remote server, keeping\u0000the monitored data secret is crucial, particularly when they contain sensitive\u0000information, e.g., biological or location data. Recently, Banno et al. (CAV'22)\u0000proposed a protocol for online LTL monitoring that keeps data concealed from\u0000the server using Fully Homomorphic Encryption (FHE). We build on this protocol\u0000to allow arithmetic operations over encrypted values, e.g., to compute a safety\u0000measurement combining distance, velocity, and so forth. Overall, our protocol\u0000enables oblivious online monitoring of discrete-time real-valued signals\u0000against signal temporal logic (STL) formulas. Our protocol combines two FHE\u0000schemes, CKKS and TFHE, leveraging their respective strengths. We employ CKKS\u0000to evaluate arithmetic predicates in STL formulas while utilizing TFHE to\u0000process them using a DFA derived from the STL formula. We conducted case\u0000studies on monitoring blood glucose levels and vehicles' behavior against the\u0000Responsibility-Sensitive Safety (RSS) rules. Our results suggest the practical\u0000relevance of our protocol.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"164 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172667","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

The Expressive Capacity of State Space Models: A Formal Language Perspective 状态空间模型的表达能力：形式语言视角

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-27 DOI: arxiv-2405.17394

Yash Sarrof, Yana Veitsman, Michael Hahn

引用次数: 0

The Power of Hard Attention Transformers on Data Sequences: A Formal Language Theoretic Perspective 数据序列上的硬注意变换器的力量：形式语言理论的视角

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-25 DOI: arxiv-2405.16166

Pascal Bergsträßer, Chris Köcher, Anthony Widjaja Lin, Georg Zetzsche

{"title":"The Power of Hard Attention Transformers on Data Sequences: A Formal Language Theoretic Perspective","authors":"Pascal Bergsträßer, Chris Köcher, Anthony Widjaja Lin, Georg Zetzsche","doi":"arxiv-2405.16166","DOIUrl":"https://doi.org/arxiv-2405.16166","url":null,"abstract":"Formal language theory has recently been successfully employed to unravel the\u0000power of transformer encoders. This setting is primarily applicable in Natural\u0000Languange Processing (NLP), as a token embedding function (where a bounded\u0000number of tokens is admitted) is first applied before feeding the input to the\u0000transformer. On certain kinds of data (e.g. time series), we want our\u0000transformers to be able to handle emph{arbitrary} input sequences of numbers\u0000(or tuples thereof) without emph{a priori} limiting the values of these\u0000numbers. In this paper, we initiate the study of the expressive power of\u0000transformer encoders on sequences of data (i.e. tuples of numbers). Our results\u0000indicate an increase in expressive power of hard attention transformers over\u0000data sequences, in stark contrast to the case of strings. In particular, we\u0000prove that Unique Hard Attention Transformers (UHAT) over inputs as data\u0000sequences no longer lie within the circuit complexity class $AC^0$ (even\u0000without positional encodings), unlike the case of string inputs, but are still\u0000within the complexity class $TC^0$ (even with positional encodings). Over\u0000strings, UHAT without positional encodings capture only regular languages. In\u0000contrast, we show that over data sequences UHAT can capture non-regular\u0000properties. Finally, we show that UHAT capture languages definable in an\u0000extension of linear temporal logic with unary numeric predicates and\u0000arithmetics.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172751","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 framework for extraction and transformation of documents 文件提取和转换框架

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-20 DOI: arxiv-2405.12350

Cristian Riveros, Markus L. Schmid, Nicole Schweikardt

{"title":"A framework for extraction and transformation of documents","authors":"Cristian Riveros, Markus L. Schmid, Nicole Schweikardt","doi":"arxiv-2405.12350","DOIUrl":"https://doi.org/arxiv-2405.12350","url":null,"abstract":"We present a theoretical framework for the extraction and transformation of\u0000text documents. We propose to use a two-phase process where the first phase\u0000extracts span-tuples from a document, and the second phase maps the content of\u0000the span-tuples into new documents. We base the extraction phase on the\u0000framework of document spanners and the transformation phase on the theory of\u0000polyregular functions, the class of regular string-to-string functions with\u0000polynomial growth. For supporting practical extract-transform scenarios, we propose an extension\u0000of document spanners described by regex formulas from span-tuples to so-called\u0000multispan-tuples, where variables are mapped to sets of spans. We prove that\u0000this extension, called regex multispanners, has the same desirable properties\u0000as standard spanners described by regex formulas. In our framework, an\u0000Extract-Transform (ET) program is given by a regex multispanner followed by a\u0000polyregular function. In this paper, we study the expressibility and evaluation problem of ET\u0000programs when the transformation function is linear, called linear ET programs.\u0000We show that linear ET programs are equally expressive as non-deterministic\u0000streaming string transducers under bag semantics. Moreover, we show that linear\u0000ET programs are closed under composition. Finally, we present an enumeration\u0000algorithm for evaluating every linear ET program over a document with linear\u0000time preprocessing and constant delay.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"222 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153467","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

Finite-valued Streaming String Transducers 有限值流字符串转换器

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-13 DOI: arxiv-2405.08171

Emmanuel Filiot, Ismaël Jecker, Gabriele Puppis, Christof Löding, Anca Muscholl, Sarah Winter

{"title":"Finite-valued Streaming String Transducers","authors":"Emmanuel Filiot, Ismaël Jecker, Gabriele Puppis, Christof Löding, Anca Muscholl, Sarah Winter","doi":"arxiv-2405.08171","DOIUrl":"https://doi.org/arxiv-2405.08171","url":null,"abstract":"A transducer is finite-valued if for some bound k, it maps any given input to\u0000at most k outputs. For classical, one-way transducers, it is known since the\u000080s that finite valuedness entails decidability of the equivalence problem.\u0000This decidability result is in contrast to the general case, which makes\u0000finite-valued transducers very attractive. For classical transducers, it is\u0000also known that finite valuedness is decidable and that any k-valued finite\u0000transducer can be decomposed as a union of k single-valued finite transducers. In this paper, we extend the above results to copyless streaming string\u0000transducers (SSTs), answering questions raised by Alur and Deshmukh in 2011.\u0000SSTs strictly extend the expressiveness of one-way transducers via additional\u0000variables that store partial outputs. We prove that any k-valued SST can be\u0000effectively decomposed as a union of k (single-valued) deterministic SSTs. As a\u0000corollary, we obtain equivalence of SSTs and two-way transducers in the\u0000finite-valued case (those two models are incomparable in general). Another\u0000corollary is an elementary upper bound for checking equivalence of\u0000finite-valued SSTs. The latter problem was already known to be decidable, but\u0000the proof complexity was unknown (it relied on Ehrenfeucht's conjecture).\u0000Finally, our main result is that finite valuedness of SSTs is decidable. The\u0000complexity is PSpace, and even PTime when the number of variables is fixed.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2010 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061052","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

Gödel Number based Clustering Algorithm with Decimal First Degree Cellular Automata 基于哥德尔数的十进制一级细胞自动机聚类算法

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-08 DOI: arxiv-2405.04881

Vicky Vikrant, Narodia Parth P, Kamalika Bhattacharjee

引用次数: 0

Planning with Probabilistic Opacity and Transparency: A Computational Model of Opaque/Transparent Observations 用概率不透明和透明规划：不透明/透明观测的计算模型

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-08 DOI: arxiv-2405.05408

Sumukha Udupa, Jie Fu

{"title":"Planning with Probabilistic Opacity and Transparency: A Computational Model of Opaque/Transparent Observations","authors":"Sumukha Udupa, Jie Fu","doi":"arxiv-2405.05408","DOIUrl":"https://doi.org/arxiv-2405.05408","url":null,"abstract":"Qualitative opacity of a secret is a security property, which means that a\u0000system trajectory satisfying the secret is observation-equivalent to a\u0000trajectory violating the secret. In this paper, we study how to synthesize a\u0000control policy that maximizes the probability of a secret being made opaque\u0000against an eavesdropping attacker/observer, while subject to other task\u0000performance constraints. In contrast to existing belief-based approach for\u0000opacity-enforcement, we develop an approach that uses the observation function,\u0000the secret, and the model of the dynamical systems to construct a so-called\u0000opaque-observations automaton which accepts the exact set of observations that\u0000enforce opacity. Leveraging this opaque-observations automaton, we can reduce\u0000the optimal planning in Markov decision processes(MDPs) for maximizing\u0000probabilistic opacity or its dual notion, transparency, subject to task\u0000constraints into a constrained planning problem over an augmented-state MDP.\u0000Finally, we illustrate the effectiveness of the developed methods in robot\u0000motion planning problems with opacity or transparency requirements.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938343","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