It is known that the Wadge reducibility of regular $omega$-languages is efficiently decidable (Krishnan et al., 1995), (Wilke, Yoo, 1995). In this paper we study analogous problem for regular k-partitions of $omega$-languages. In the series of previous papers (Selivanov, 2011), (Alaev, Selivanov, 2021), (Selivanov, 2012) there was a partial progress towards obtaining an efficient algorithm for deciding the Wadge reducibility in this setting as well. In this paper we finalize this line of research providing a quadratic algorithm (in RAM model). For this we construct a quadratic algorithm to decide a preorder relation on iterated posets. Additionally, we discuss the size of the representation of regular $omega$-languages and suggest a more compact way to represent them. The algorithm we provide is efficient for the more compact representation as well.
{"title":"Complexity Aspects of the Extension of Wagner's Hierarchy to $k$-Partitions","authors":"Vladimir Podolskii, Victor Selivanov","doi":"arxiv-2409.06977","DOIUrl":"https://doi.org/arxiv-2409.06977","url":null,"abstract":"It is known that the Wadge reducibility of regular $omega$-languages is\u0000efficiently decidable (Krishnan et al., 1995), (Wilke, Yoo, 1995). In this\u0000paper we study analogous problem for regular k-partitions of\u0000$omega$-languages. In the series of previous papers (Selivanov, 2011), (Alaev,\u0000Selivanov, 2021), (Selivanov, 2012) there was a partial progress towards\u0000obtaining an efficient algorithm for deciding the Wadge reducibility in this\u0000setting as well. In this paper we finalize this line of research providing a\u0000quadratic algorithm (in RAM model). For this we construct a quadratic algorithm\u0000to decide a preorder relation on iterated posets. Additionally, we discuss the\u0000size of the representation of regular $omega$-languages and suggest a more\u0000compact way to represent them. The algorithm we provide is efficient for the\u0000more compact representation as well.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225204","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}
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a higher complexity than in the string case. Top-down as well as bottom-up deterministic DAG languages are subclasses of the regular DAG languages. We refine this hierarchy by providing a weaker subclass of the deterministic DAG languages. For a DAG grammar generating a language in this new DAG language class, or, equivalently, a DAG-automaton recognizing it, a classical deterministic finite state automaton (DFA) can be constructed. As the main result, we provide a characterization of this class. The motivation behind this is the transfer of techniques for regular string languages to graphs. Trivially, our restricted DAG language class is closed under union and intersection. This permits the application of minimization and hyper-minimization algorithms known for DFAs. This alternative notion of regularity coins at the existence of a DFA for recognizing a DAG language.
与正则字符串语言和树语言类似，文献中也定义了有向环图（DAG）的正则语言。虽然这些 DAG 语言被称为正则语言，但它们的功能更强大，因此标准问题的复杂度比字符串语言更高。自上而下和自下而上的确定性 DAG 语言都是规则 DAG 语言的子类。我们通过提供一个较弱的确定性 DAG 语言子类来细化这一层次结构。对于生成这种新 DAG 语言类中的语言的 DAG 语法，或者等价于识别这种语言的 DAG 自动机，可以构造经典的确定性有限状态自动机（DFA）。作为主要成果，我们提供了该类的特征描述。这背后的动机是将正则字符串语言的技术转移到图中。简单地说，我们的受限 DAG 语言类在联合和交集下是封闭的。这就允许应用已知的 DFA 最小化和超最小化算法。这种另类的不规则性概念寄希望于识别 DAG 语言的 DFA 的存在。
{"title":"A New Notion of Regularity: Finite State Automata Accepting Graphs","authors":"Yvo Ad MeeresUniversity of Bremen, Germany","doi":"arxiv-2409.06968","DOIUrl":"https://doi.org/arxiv-2409.06968","url":null,"abstract":"Analogous to regular string and tree languages, regular languages of directed\u0000acyclic graphs (DAGs) are defined in the literature. Although called regular,\u0000those DAG-languages are more powerful and, consequently, standard problems have\u0000a higher complexity than in the string case. Top-down as well as bottom-up\u0000deterministic DAG languages are subclasses of the regular DAG languages. We\u0000refine this hierarchy by providing a weaker subclass of the deterministic DAG\u0000languages. For a DAG grammar generating a language in this new DAG language\u0000class, or, equivalently, a DAG-automaton recognizing it, a classical\u0000deterministic finite state automaton (DFA) can be constructed. As the main\u0000result, we provide a characterization of this class. The motivation behind this is the transfer of techniques for regular string\u0000languages to graphs. Trivially, our restricted DAG language class is closed\u0000under union and intersection. This permits the application of minimization and\u0000hyper-minimization algorithms known for DFAs. This alternative notion of\u0000regularity coins at the existence of a DFA for recognizing a DAG language.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197190","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}
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the upper bounds of operational state complexity known for finite languages apply for block languages as well. However, in several cases, smaller values were found. Block languages can be represented as bitmaps, which are a good tool to study their minimal finite automata and their operations, as we illustrate here.
{"title":"Operational State Complexity of Block Languages","authors":"Guilherme DuarteCMUP & FCUP, Nelma MoreiraCMUP & FCUP, Luca PrigionieroUniversity of Loughborough, Rogério ReisCMUP & FCUP","doi":"arxiv-2409.06970","DOIUrl":"https://doi.org/arxiv-2409.06970","url":null,"abstract":"In this paper we consider block languages, namely sets of words having the\u0000same length, and study the deterministic and nondeterministic state complexity\u0000of several operations on these languages. Being a subclass of finite languages,\u0000the upper bounds of operational state complexity known for finite languages\u0000apply for block languages as well. However, in several cases, smaller values\u0000were found. Block languages can be represented as bitmaps, which are a good\u0000tool to study their minimal finite automata and their operations, as we\u0000illustrate here.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197188","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}
František MrázCharles University at Prague, Friedrich OttoUniversity of Kassel
Here we propose an extension of the (deterministic and the nondeterministic) finite automaton with translucent letters (DFAwtl and NFAwtl), which lies between these automata and their non-returning variants (that is, the nr-DFAwtl and the nr-NFAwtl). This new model works like a DFAwtl or an NFAwtl, but on seeing the end-of-tape marker, it may change its internal state and continue with its computation instead of just ending it, accepting or rejecting. This new type of automaton is called a repetitive deterministic or nondeterministic finite automaton with translucent letters (RDFAwtl or RNFAwtl). In the deterministic case, the new model is strictly more expressive than the DFAwtl, but less expressive than the nr-DFAwtl, while in the nondeterministic case, the new model is equivalent to the NFAwtl.
{"title":"Repetitive Finite Automata With Translucent Letters","authors":"František MrázCharles University at Prague, Friedrich OttoUniversity of Kassel","doi":"arxiv-2409.06975","DOIUrl":"https://doi.org/arxiv-2409.06975","url":null,"abstract":"Here we propose an extension of the (deterministic and the nondeterministic)\u0000finite automaton with translucent letters (DFAwtl and NFAwtl), which lies\u0000between these automata and their non-returning variants (that is, the nr-DFAwtl\u0000and the nr-NFAwtl). This new model works like a DFAwtl or an NFAwtl, but on\u0000seeing the end-of-tape marker, it may change its internal state and continue\u0000with its computation instead of just ending it, accepting or rejecting. This\u0000new type of automaton is called a repetitive deterministic or nondeterministic\u0000finite automaton with translucent letters (RDFAwtl or RNFAwtl). In the\u0000deterministic case, the new model is strictly more expressive than the DFAwtl,\u0000but less expressive than the nr-DFAwtl, while in the nondeterministic case, the\u0000new model is equivalent to the NFAwtl.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197183","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}
Martin KutribInstitut für Informatik, Universität Giessen, Andreas MalcherInstitut für Informatik, Universität Giessen, Matthias WendlandtInstitut für Informatik, Universität Giessen
Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with a special acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than one accepting paths, the input is rejected. We study the descriptional complexity of XNFA accepting unary languages. While the state costs for mutual simulations with DFA and NFA over general alphabets differ significantly from the known types of finite automata, it turns out that the state costs for the simulations in the unary case are in the order of magnitude of the general case. In particular, the state costs for the simulation of an XNFA by a DFA or an NFA are $e^{theta(sqrt{n cdot ln{n}})}$. Conversely, converting an NFA to an equivalent XNFA may cost $e^{theta(sqrt{n cdot ln{n}})}$ states as well. All bounds obtained are also tight in the order of magnitude. Finally, we investigate the computational complexity of different decision problems for unary XNFA and it is shown that the problems of emptiness, universality, inclusion, and equivalence are coNP-complete, whereas the general membership problem is NL-complete.
{"title":"Complexity of Unary Exclusive Nondeterministic Finite Automata","authors":"Martin KutribInstitut für Informatik, Universität Giessen, Andreas MalcherInstitut für Informatik, Universität Giessen, Matthias WendlandtInstitut für Informatik, Universität Giessen","doi":"arxiv-2409.06967","DOIUrl":"https://doi.org/arxiv-2409.06967","url":null,"abstract":"Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite\u0000automata with a special acceptance condition. An input is accepted if there is\u0000exactly one accepting path in its computation tree. If there are none or more\u0000than one accepting paths, the input is rejected. We study the descriptional\u0000complexity of XNFA accepting unary languages. While the state costs for mutual\u0000simulations with DFA and NFA over general alphabets differ significantly from\u0000the known types of finite automata, it turns out that the state costs for the\u0000simulations in the unary case are in the order of magnitude of the general\u0000case. In particular, the state costs for the simulation of an XNFA by a DFA or\u0000an NFA are $e^{theta(sqrt{n cdot ln{n}})}$. Conversely, converting an NFA to\u0000an equivalent XNFA may cost $e^{theta(sqrt{n cdot ln{n}})}$ states as well.\u0000All bounds obtained are also tight in the order of magnitude. Finally, we\u0000investigate the computational complexity of different decision problems for\u0000unary XNFA and it is shown that the problems of emptiness, universality,\u0000inclusion, and equivalence are coNP-complete, whereas the general membership\u0000problem is NL-complete.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225205","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}
Benedek NagyEastern Mediterranean University, Famagusta and Eszterházy Károly Catholic University, Eger
Watson-Crick (WK) finite automata work on a Watson-Crick tape representing a DNA molecule. They have two reading heads. In 5'->3' WK automata, the heads move and read the input in opposite physical directions. In this paper, we consider such inputs which are necklaces, i.e., they represent circular DNA molecules. In sensing 5'->3' WK automata, the computation on the input is finished when the heads meet. As the original model is capable of accepting the linear context-free languages, the necklace languages we are investigating here have strong relations to that class. Here, we use these automata in two different acceptance modes. On the one hand, in weak acceptance mode the heads are starting nondeterministically at any point of the input, like the necklace is cut at a nondeterministically chosen point), and if the input is accepted, it is in the accepted necklace language. These languages can be seen as the languages obtained from the linear context-free languages by taking their closure under cyclic shift operation. On the other hand, in strong acceptance mode, it is required that the input is accepted starting the heads in the computation from every point of the cycle. These languages can be seen as the maximal cyclic shift closed languages included in a linear language. On the other hand, as it will be shown, they have a kind of locally testable property. We present some hierarchy results based on restricted variants of the WK automata, such as stateless or all-final variants.
沃森-克里克（WK）有限自动机在代表 DNA 分子的沃森-克里克磁带上工作。它们有两个读取头。在 5'->3' WK 自动机中，读头以相反的物理方向移动并读取输入。在本文中，我们考虑的输入是项链，即代表环形 DNA 分子。在传感 5'->3' WK 自动机中，输入的计算在头相遇时完成。由于原始模型能够接受线性无上下文语言，我们在此研究的项链语言与该类语言有密切关系。在这里，我们在两种不同的接受模式下使用这些自动机。一方面，在弱接受模式中，头是在输入的任意点上不确定地开始的，就像项链是在不确定地选择的点上剪断的），如果输入被接受，它就是在被接受的项链语言中。这些语言可以看作是线性无上下文语言在循环移位运算下取其封闭性而得到的语言。另一方面，在强接受模式下，要求输入被接受后，从循环的每一点开始计算。这些语言可以看作是包含在线性语言中的最大循环移位封闭语言。我们将介绍一些基于 WKautomata 受限变体（如无状态变体或全终结变体）的层次结果。
{"title":"5' -> 3' Watson-Crick Automata accepting Necklaces","authors":"Benedek NagyEastern Mediterranean University, Famagusta and Eszterházy Károly Catholic University, Eger","doi":"arxiv-2409.06976","DOIUrl":"https://doi.org/arxiv-2409.06976","url":null,"abstract":"Watson-Crick (WK) finite automata work on a Watson-Crick tape representing a\u0000DNA molecule. They have two reading heads. In 5'->3' WK automata, the heads\u0000move and read the input in opposite physical directions. In this paper, we\u0000consider such inputs which are necklaces, i.e., they represent circular DNA\u0000molecules. In sensing 5'->3' WK automata, the computation on the input is\u0000finished when the heads meet. As the original model is capable of accepting the\u0000linear context-free languages, the necklace languages we are investigating here\u0000have strong relations to that class. Here, we use these automata in two\u0000different acceptance modes. On the one hand, in weak acceptance mode the heads\u0000are starting nondeterministically at any point of the input, like the necklace\u0000is cut at a nondeterministically chosen point), and if the input is accepted,\u0000it is in the accepted necklace language. These languages can be seen as the\u0000languages obtained from the linear context-free languages by taking their\u0000closure under cyclic shift operation. On the other hand, in strong acceptance\u0000mode, it is required that the input is accepted starting the heads in the\u0000computation from every point of the cycle. These languages can be seen as the\u0000maximal cyclic shift closed languages included in a linear language. On the\u0000other hand, as it will be shown, they have a kind of locally testable property.\u0000We present some hierarchy results based on restricted variants of the WK\u0000automata, such as stateless or all-final variants.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197182","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}
Parikh (tree) automata are an expressive and yet computationally well-behaved extension of finite automata -- they allow to increment a number of counters during their computations, which are finally tested by a semilinear constraint. In this work, we introduce and investigate a new perspective on Parikh tree automata (PTA): instead of testing one counter configuration that results from the whole input tree, we implement a non-global automaton model. Here, we copy and distribute the current configuration at each node to all its children, incrementing the counters pathwise, and check the arithmetic constraint at each leaf. We obtain that the classes of tree languages recognizable by global PTA and non-global PTA are incomparable. In contrast to global PTA, the non-emptiness problem is undecidable for non-global PTA if we allow the automata to work with at least three counters, whereas the membership problem stays decidable. However, for a restriction of the model, where counter configurations are passed in a linear fashion to at most one child node, we can prove decidability of the non-emptiness problem.
{"title":"Non-Global Parikh Tree Automata","authors":"Luisa HerrmannTU Dresden, Johannes Osterholzer","doi":"arxiv-2409.06973","DOIUrl":"https://doi.org/arxiv-2409.06973","url":null,"abstract":"Parikh (tree) automata are an expressive and yet computationally well-behaved\u0000extension of finite automata -- they allow to increment a number of counters\u0000during their computations, which are finally tested by a semilinear constraint.\u0000In this work, we introduce and investigate a new perspective on Parikh tree\u0000automata (PTA): instead of testing one counter configuration that results from\u0000the whole input tree, we implement a non-global automaton model. Here, we copy\u0000and distribute the current configuration at each node to all its children,\u0000incrementing the counters pathwise, and check the arithmetic constraint at each\u0000leaf. We obtain that the classes of tree languages recognizable by global PTA\u0000and non-global PTA are incomparable. In contrast to global PTA, the\u0000non-emptiness problem is undecidable for non-global PTA if we allow the\u0000automata to work with at least three counters, whereas the membership problem\u0000stays decidable. However, for a restriction of the model, where counter\u0000configurations are passed in a linear fashion to at most one child node, we can\u0000prove decidability of the non-emptiness problem.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197185","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}
The Fourteenth International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024) was held in G"ottingen, Germany, on August 12 and 13, 2024, at the historic Georg-Augustus-Universit"at, organized by the Theoretical Computer Science research group of the respective university. The NCMA workshop series was established in 2009 as an annual event for researchers working on non-classical and classical models of automata, grammars or related devices. Such models are investigated both as theoretical models and as formal models for applications from various points of view. The goal of the NCMA workshop series is to exchange and develop novel ideas in order to gain deeper and interdisciplinary coverage of this particular area that may foster new insights and substantial progress.
{"title":"Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)","authors":"Florin Manea, Giovanni Pighizzini","doi":"arxiv-2409.06120","DOIUrl":"https://doi.org/arxiv-2409.06120","url":null,"abstract":"The Fourteenth International Workshop on Non-Classical Models of Automata and\u0000Applications (NCMA 2024) was held in G\"ottingen, Germany, on August 12 and 13,\u00002024, at the historic Georg-Augustus-Universit\"at, organized by the\u0000Theoretical Computer Science research group of the respective university. The\u0000NCMA workshop series was established in 2009 as an annual event for researchers\u0000working on non-classical and classical models of automata, grammars or related\u0000devices. Such models are investigated both as theoretical models and as formal\u0000models for applications from various points of view. The goal of the NCMA\u0000workshop series is to exchange and develop novel ideas in order to gain deeper\u0000and interdisciplinary coverage of this particular area that may foster new\u0000insights and substantial progress.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197214","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}
In this paper, we consider partially observable timed automata endowed with a single clock. A time interval is associated with each transition specifying at which clock values it may occur. In addition, a resetting condition associated to a transition specifies how the clock value is updated upon its occurrence. This work deals with the estimation of the current state given a timed observation, i.e., a succession of pairs of an observable event and the time instant at which the event has occurred. The problem of state reachability in the timed automaton is reduced to the reachability analysis of the associated zone automaton, which provides a purely discrete event description of the behaviour of the timed automaton. An algorithm is formulated to provide an offline approach for state estimation of a timed automaton based on the assumption that the clock is reset upon the occurrence of each observable transition.
{"title":"State estimation of timed automata under partial observation [Draft version]","authors":"Chao Gao, Dimitri Lefebvre, Carla Seatzu, Zhiwu Li, Alessandro Giua","doi":"arxiv-2409.05810","DOIUrl":"https://doi.org/arxiv-2409.05810","url":null,"abstract":"In this paper, we consider partially observable timed automata endowed with a\u0000single clock. A time interval is associated with each transition specifying at\u0000which clock values it may occur. In addition, a resetting condition associated\u0000to a transition specifies how the clock value is updated upon its occurrence.\u0000This work deals with the estimation of the current state given a timed\u0000observation, i.e., a succession of pairs of an observable event and the time\u0000instant at which the event has occurred. The problem of state reachability in\u0000the timed automaton is reduced to the reachability analysis of the associated\u0000zone automaton, which provides a purely discrete event description of the\u0000behaviour of the timed automaton. An algorithm is formulated to provide an\u0000offline approach for state estimation of a timed automaton based on the\u0000assumption that the clock is reset upon the occurrence of each observable\u0000transition.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197215","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}
Alessandro Cimatti, Thomas M. Grosen, Kim G. Larsen, Stefano Tonetta, Martin Zimmermann
Runtime verification of temporal properties over timed sequences of observations is crucial in various applications within cyber-physical systems ranging from autonomous vehicles over smart grids to medical devices. In this paper, we are addressing the challenge of effectively predicting the failure or success of properties in a continuous real-time setting. Our approach allows predictions to exploit assumptions on the system being monitored and supports predictions of non-observable system behaviour (e.g. internal faults). More concretely, in our approach properties are expressed in Metric Interval Temporal Logic (MITL), assumptions on the monitored system are specified in terms of Timed Automata, and observations are to be provided in terms of sequences of timed constraints. We present an assumption-based runtime verification algorithm and its implementation on top of the real-time verification tool UPPAAL. We show experimentally that assumptions can be effective in anticipating the satisfaction/violation of timed properties and in handling monitoring properties that predicate over unobservable events.
{"title":"Exploiting Assumptions for Effective Monitoring of Real-Time Properties under Partial Observability","authors":"Alessandro Cimatti, Thomas M. Grosen, Kim G. Larsen, Stefano Tonetta, Martin Zimmermann","doi":"arxiv-2409.05456","DOIUrl":"https://doi.org/arxiv-2409.05456","url":null,"abstract":"Runtime verification of temporal properties over timed sequences of\u0000observations is crucial in various applications within cyber-physical systems\u0000ranging from autonomous vehicles over smart grids to medical devices. In this\u0000paper, we are addressing the challenge of effectively predicting the failure or\u0000success of properties in a continuous real-time setting. Our approach allows\u0000predictions to exploit assumptions on the system being monitored and supports\u0000predictions of non-observable system behaviour (e.g. internal faults). More\u0000concretely, in our approach properties are expressed in Metric Interval\u0000Temporal Logic (MITL), assumptions on the monitored system are specified in\u0000terms of Timed Automata, and observations are to be provided in terms of\u0000sequences of timed constraints. We present an assumption-based runtime\u0000verification algorithm and its implementation on top of the real-time\u0000verification tool UPPAAL. We show experimentally that assumptions can be\u0000effective in anticipating the satisfaction/violation of timed properties and in\u0000handling monitoring properties that predicate over unobservable events.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197216","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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