{"title":"Two or three things I know about tree transducers","authors":"Lê Thành Dũng Nguyên","doi":"arxiv-2409.03169","DOIUrl":"https://doi.org/arxiv-2409.03169","url":null,"abstract":"You might know that the name \"tree transducers\" refers to various kinds of\u0000automata that compute functions on ranked trees, i.e. terms over a first-order\u0000signature. But have you ever wondered about how to remember what a macro tree transducer\u0000does? Or what are the connections between top-down tree(-to-string)\u0000transducers, multi bottom-up tree(-to-string) transducers, tree-walking\u0000transducers, (invisible) pebble tree transducers, monadic second-order\u0000transductions, unfoldings of rooted directed acyclic graphs (i.e. term graphs)\u0000-- and what happens when the functions that they compute are composed? The answers may be found in old papers (mostly coauthored by Engelfriet), but\u0000maybe you can save some time by first looking at this short note.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225206","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}
Marek Chalupa, Thomas A. Henzinger, Nicolas Mazzocchi, N. Ege Saraç
{"title":"QuAK: Quantitative Automata Kit","authors":"Marek Chalupa, Thomas A. Henzinger, Nicolas Mazzocchi, N. Ege Saraç","doi":"arxiv-2409.03569","DOIUrl":"https://doi.org/arxiv-2409.03569","url":null,"abstract":"System behaviors are traditionally evaluated through binary classifications\u0000of correctness, which do not suffice for properties involving quantitative\u0000aspects of systems and executions. Quantitative automata offer a more nuanced\u0000approach, mapping each execution to a real number by incorporating weighted\u0000transitions and value functions generalizing acceptance conditions. In this\u0000paper, we introduce QuAK, the first tool designed to automate the analysis of\u0000quantitative automata. QuAK currently supports a variety of quantitative\u0000automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg\u0000automata, and implements decision procedures for problems such as emptiness,\u0000universality, inclusion, equivalence, as well as for checking whether an\u0000automaton is safe, live, or constant. Additionally, QuAK is able to compute\u0000extremal values when possible, construct safety-liveness decompositions, and\u0000monitor system behaviors. We demonstrate the effectiveness of QuAK through\u0000experiments focusing on the inclusion, constant-function check, and monitoring\u0000problems.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197217","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}
A. Ramírez-de-Arellano, F. G. C. Cabarle, D. Orellana-Martín, M. J. Pérez-Jiménez
{"title":"Normal forms in Virus Machines","authors":"A. Ramírez-de-Arellano, F. G. C. Cabarle, D. Orellana-Martín, M. J. Pérez-Jiménez","doi":"arxiv-2409.03327","DOIUrl":"https://doi.org/arxiv-2409.03327","url":null,"abstract":"In the present work, we further study the computational power of virus\u0000machines (VMs in short). VMs provide a computing paradigm inspired by the\u0000transmission and replication networks of viruses. VMs consist of process units\u0000(called hosts) structured by a directed graph whose arcs are called channels\u0000and an instruction graph that controls the transmissions of virus objects among\u0000hosts. The present work complements our understanding of the computing power of\u0000VMs by introducing normal forms; these expressions restrict the features in a\u0000given computing model. Some of the features that we restrict in our normal\u0000forms include (a) the number of hosts, (b) the number of instructions, and (c)\u0000the number of virus objects in each host. After we recall some known results on\u0000the computing power of VMs we give our normal forms, such as the size of the\u0000loops in the network, proving new characterisations of family of sets, such as\u0000the finite sets, semilinear sets, or NRE.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197219","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}
Giann Karlo Aguirre Samboni, Stefan Haar, Loic Paulevé, Stefan Schwoon, Nick Würdemann
{"title":"Attractor Basins in Concurrent Systems","authors":"Giann Karlo Aguirre Samboni, Stefan Haar, Loic Paulevé, Stefan Schwoon, Nick Würdemann","doi":"arxiv-2409.01079","DOIUrl":"https://doi.org/arxiv-2409.01079","url":null,"abstract":"A crucial question in analyzing a concurrent system is to determine its\u0000long-run behaviour, and in particular, whether there are irreversible choices\u0000in its evolution, leading into parts of the reachability space from which there\u0000is no return to other parts. Casting this problem in the unifying framework of\u0000safe Petri nets, our previous work has provided techniques for identifying\u0000attractors, i.e. terminal strongly connected components of the reachability\u0000space. What we aim at is to determine the attraction basins associated to those\u0000attractors; that is, those states from where all infinite runs are doomed to\u0000end in the given attractor, as opposed to those that are free to evolve\u0000differently. Here, we provide a solution for the case of safe Petri nets. Our\u0000algorithm uses net unfoldings and provides a map of all of those configurations\u0000(concurrent executions of the system) that lead onto cliff-edges, i.e. any\u0000maximal extension for those configurations lies in some basin that is\u0000considered fatal.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197218","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}
{"title":"Imposing Rules in Process Discovery: an Inductive Mining Approach","authors":"Ali Norouzifar, Marcus Dees, Wil van der Aalst","doi":"arxiv-2408.17326","DOIUrl":"https://doi.org/arxiv-2408.17326","url":null,"abstract":"Process discovery aims to discover descriptive process models from event\u0000logs. These discovered process models depict the actual execution of a process\u0000and serve as a foundational element for conformance checking, performance\u0000analyses, and many other applications. While most of the current process\u0000discovery algorithms primarily rely on a single event log for model discovery,\u0000additional sources of information, such as process documentation and domain\u0000experts' knowledge, remain untapped. This valuable information is often\u0000overlooked in traditional process discovery approaches. In this paper, we\u0000propose a discovery technique incorporating such knowledge in a novel inductive\u0000mining approach. This method takes a set of user-defined or discovered rules as\u0000input and utilizes them to discover enhanced process models. Our proposed\u0000framework has been implemented and tested using several publicly available\u0000real-life event logs. Furthermore, to showcase the framework's effectiveness in\u0000a practical setting, we conducted a case study in collaboration with UWV, the\u0000Dutch employee insurance agency.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197220","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}
{"title":"Matching walks that are minimal with respect to edge inclusion","authors":"Victor Marsault","doi":"arxiv-2408.14048","DOIUrl":"https://doi.org/arxiv-2408.14048","url":null,"abstract":"In this paper we show that enumerating the set MM(G,R), defined below, cannot\u0000be done with polynomial-delay in its input G and R, unless P=NP. R is a regular\u0000expression over an alphabet $Sigma$, G is directed graph labeled over\u0000$Sigma$, and MM(G,R) contains walks of G. First, consider the set Match(G,R)\u0000containing all walks G labeled by a word (over $Sigma$) that conforms to $R$.\u0000In general, M(G,R) is infinite, and MM(G,R) is the finite subset of Match(G,R)\u0000of the walks that are minimal according to a well-quasi-order <. It holds w<w'\u0000if the multiset of edges appearing in w is strictly included in the multiset of\u0000edges appearing in w'. Remarkably, the set MM(G,R) contains some walks that may\u0000be computed in polynomial time. Hence, it is not the case that the\u0000preprocessing phase of any algorithm enumerating MM(G,R) must solve an NP-hard\u0000problem.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"267 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197221","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}
{"title":"Exponent-Strings and Their Edit Distance","authors":"Ingyu Baek","doi":"arxiv-2408.12931","DOIUrl":"https://doi.org/arxiv-2408.12931","url":null,"abstract":"An exponent-string is an extension of traditional strings that can\u0000incorporate real-numbered exponents, indicating the quantity of characters.\u0000This novel representation overcomes the limitations of traditional discrete\u0000string by enabling precise data representation for applications such as\u0000phonetic transcription that contains sound duration. Although applications of exponent-string are focused on exponent-string with\u0000real-numbered exponents, formal definition uses arbitrary semigroup. For any\u0000semigroup $S$, $S$-exponent-strings are allowed to have elements of $S$ as\u0000exponents. We investigate algebraic properties of $S$-exponent-strings and\u0000further justify $mathbb{R}^+$-exponent-string is a natural extension of the\u0000string. Motivated by the problem of calculating the similarity between spoken phone\u0000sequence and correct phone sequence, we develop exp-edit distance -- a\u0000specialized metric designed to measure the similarity between\u0000$mathbb{R}^+$-exponent-strings. By extending the traditional string edit\u0000distance to handle continuous values, exp-edit distance deals with\u0000$mathbb{R}^+$-exponent-strings that embody both discrete and continuous\u0000properties. Our exploration includes a rigorous mathematical formulation of\u0000exp-edit distance and an algorithm to compute it.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197222","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}
{"title":"Greybox Learning of Languages Recognizable by Event-Recording Automata","authors":"Anirban Majumdar, Sayan Mukherjee, Jean-François Raskin","doi":"arxiv-2408.12551","DOIUrl":"https://doi.org/arxiv-2408.12551","url":null,"abstract":"In this paper, we revisit the active learning of timed languages recognizable\u0000by event-recording automata. Our framework employs a method known as greybox\u0000learning, which enables the learning of event-recording automata with a minimal\u0000number of control states. This approach avoids learning the region automaton\u0000associated with the language, contrasting with existing methods. We have\u0000implemented our greybox learning algorithm with various heuristics to maintain\u0000low computational complexity. The efficacy of our approach is demonstrated\u0000through several examples.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197224","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}
{"title":"Distribution of Reconfiguration Languages maintaining Tree-like Communication Topology","authors":"Daniel Hausmann, Mathieu Lehaut, Nir Piterman","doi":"arxiv-2408.10708","DOIUrl":"https://doi.org/arxiv-2408.10708","url":null,"abstract":"We study how to distribute trace languages in a setting where processes\u0000communicate via reconfigurable communication channels. That is, the different\u0000processes can connect and disconnect from channels at run time. We restrict\u0000attention to communication via tree-like communication architectures. These\u0000allow channels to connect more than two processes in a way that maintains an\u0000underlying spanning tree and keeps communication continuous on the tree. We\u0000make the reconfiguration explicit in the language allowing both a centralized\u0000automaton as well as the distributed processes to share relevant information\u0000about the current communication configuration. We show that Zielonka's seminal\u0000result regarding distribution of regular languages for asynchronous automata\u0000can be generalized in this setting, incorporating both reconfiguration and more\u0000than binary tree architectures.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197226","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}
{"title":"Exploring Complexity: An Extended Study of Formal Properties for Process Model Complexity Measures","authors":"Patrizia Schalk, Adam Burke, Robert Lorenz","doi":"arxiv-2408.09871","DOIUrl":"https://doi.org/arxiv-2408.09871","url":null,"abstract":"A good process model is expected not only to reflect the behavior of the\u0000process, but also to be as easy to read and understand as possible. Because\u0000preferences vary across different applications, numerous measures provide ways\u0000to reflect the complexity of a model with a numeric score. However, this\u0000abundance of different complexity measures makes it difficult to select one for\u0000analysis. Furthermore, most complexity measures are defined for BPMN or EPC,\u0000but not for workflow nets. This paper is an extended analysis of complexity measures and their formal\u0000properties. It adapts existing complexity measures to the world of workflow\u0000nets. It then compares these measures with a set of properties originally\u0000defined for software complexity, as well as new extensions to it. We discuss\u0000the importance of the properties in theory by evaluating whether matured\u0000complexity measures should fulfill them or whether they are optional. We find\u0000that not all inspected properties are mandatory, but also demonstrate that the\u0000behavior of evolutionary process discovery algorithms is influenced by some of\u0000these properties. Our findings help analysts to choose the right complexity\u0000measure for their use-case.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197223","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}
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