{"title":"Non-deterministic, probabilistic, and quantum effects through the lens of event structures (Technical report)","authors":"Vítor Fernandes, Marc de Visme, Benoît Valiron","doi":"arxiv-2408.14563","DOIUrl":"https://doi.org/arxiv-2408.14563","url":null,"abstract":"In this paper, we consider event structures and their probabilistic and\u0000quantum extensions as originally defined by Winskel. If these structures have\u0000already been part of sophisticated computational models, they have rarely been\u0000directly studied as an immediate model of execution traces of programs. This\u0000paper offers such an analysis. We propose a simple imperative operational\u0000framework and show how to derive soundness and adequacy results with event\u0000structures considered as a semantics. We show how event structures naturally\u0000handle non-deterministic, probabilistic and quantum effects.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192526","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":"Instrumenting Transaction Trace Properties in Smart Contracts: Extending the EVM for Real-Time Security","authors":"Zhiyang Chen, Jan Gorzny, Martin Derka","doi":"arxiv-2408.14621","DOIUrl":"https://doi.org/arxiv-2408.14621","url":null,"abstract":"In the realm of smart contract security, transaction malice detection has\u0000been able to leverage properties of transaction traces to identify hacks with\u0000high accuracy. However, these methods cannot be applied in real-time to revert\u0000malicious transactions. Instead, smart contracts are often instrumented with\u0000some safety properties to enhance their security. However, these instrumentable\u0000safety properties are limited and fail to block certain types of hacks such as\u0000those which exploit read-only re-entrancy. This limitation primarily stems from\u0000the Ethereum Virtual Machine's (EVM) inability to allow a smart contract to\u0000read transaction traces in real-time. Additionally, these instrumentable safety\u0000properties can be gas-intensive, rendering them impractical for on-the-fly\u0000validation. To address these challenges, we propose modifications to both the\u0000EVM and Ethereum clients, enabling smart contracts to validate these\u0000transaction trace properties in real-time without affecting traditional EVM\u0000execution. We also use past-time linear temporal logic (PLTL) to formalize\u0000transaction trace properties, showcasing that most existing detection metrics\u0000can be expressed using PLTL. We also discuss the potential implications of our\u0000proposed modifications, emphasizing their capacity to significantly enhance\u0000smart contract security.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192516","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":"Logic interpretations of ANN partition cells","authors":"Ingo Schmitt","doi":"arxiv-2408.14314","DOIUrl":"https://doi.org/arxiv-2408.14314","url":null,"abstract":"Consider a binary classification problem solved using a feed-forward\u0000artificial neural network (ANN). Let the ANN be composed of a ReLU layer and\u0000several linear layers (convolution, sum-pooling, or fully connected). We assume\u0000the network was trained with high accuracy. Despite numerous suggested\u0000approaches, interpreting an artificial neural network remains challenging for\u0000humans. For a new method of interpretation, we construct a bridge between a\u0000simple ANN and logic. As a result, we can analyze and manipulate the semantics\u0000of an ANN using the powerful tool set of logic. To achieve this, we decompose\u0000the input space of the ANN into several network partition cells. Each network\u0000partition cell represents a linear combination that maps input values to a\u0000classifying output value. For interpreting the linear map of a partition cell\u0000using logic expressions, we suggest minterm values as the input of a simple\u0000ANN. We derive logic expressions representing interaction patterns for\u0000separating objects classified as 1 from those classified as 0. To facilitate an\u0000interpretation of logic expressions, we present them as binary logic trees.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"395 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192525","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":"Temporal Ensemble Logic","authors":"Guo-Qiang Zhang","doi":"arxiv-2408.14443","DOIUrl":"https://doi.org/arxiv-2408.14443","url":null,"abstract":"We introduce Temporal Ensemble Logic (TEL), a monadic, first-order modal\u0000logic for linear-time temporal reasoning. TEL includes primitive temporal\u0000constructs such as ``always up to $t$ time later'' ($Box_t$), ``sometimes\u0000before $t$ time in the future'' ($Diamond_t$), and ``$t$-time later''\u0000$varphi_t$. TEL has been motivated from the requirement for rigor and\u0000reproducibility for cohort specification and discovery in clinical and\u0000population health research, to fill a gap in formalizing temporal reasoning in\u0000biomedicine. In this paper, we first introduce TEL in a general set up, with\u0000discrete and dense time as special cases. We then focus on the theoretical\u0000development of discrete TEL on the temporal domain of positive integers\u0000$mathbb{N}^+$, denoted as ${rm TEL}_{mathbb{N}^+}$. ${rm\u0000TEL}_{mathbb{N}^+}$ is strictly more expressive than the standard monadic\u0000second order logic, characterized by B\"{u}chi automata. We present its formal\u0000semantics, a proof system, and provide a proof for the undecidability of the\u0000satisfiability of ${rm TEL}_{mathbb{N}^+}$. We also discuss expressiveness\u0000and decidability fragments for ${rm TEL}_{mathbb{N}^+}$, followed by\u0000illustrative applications.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192519","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}
Jan Jakubův, Mikoláš Janota, Jelle Piepenbrock, Josef Urban
{"title":"Machine Learning for Quantifier Selection in cvc5","authors":"Jan Jakubův, Mikoláš Janota, Jelle Piepenbrock, Josef Urban","doi":"arxiv-2408.14338","DOIUrl":"https://doi.org/arxiv-2408.14338","url":null,"abstract":"In this work we considerably improve the state-of-the-art SMT solving on\u0000first-order quantified problems by efficient machine learning guidance of\u0000quantifier selection. Quantifiers represent a significant challenge for SMT and\u0000are technically a source of undecidability. In our approach, we train an\u0000efficient machine learning model that informs the solver which quantifiers\u0000should be instantiated and which not. Each quantifier may be instantiated\u0000multiple times and the set of the active quantifiers changes as the solving\u0000progresses. Therefore, we invoke the ML predictor many times, during the whole\u0000run of the solver. To make this efficient, we use fast ML models based on\u0000gradient boosting decision trees. We integrate our approach into the\u0000state-of-the-art cvc5 SMT solver and show a considerable increase of the\u0000system's holdout-set performance after training it on a large set of\u0000first-order problems collected from the Mizar Mathematical Library.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192524","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}
Manuel Bodirsky, Marcin Kozik, Florent Madelaine, Barnaby Martin, Michal Wrona
{"title":"Model-checking positive equality free logic on a fixed structure (direttissima)","authors":"Manuel Bodirsky, Marcin Kozik, Florent Madelaine, Barnaby Martin, Michal Wrona","doi":"arxiv-2408.13840","DOIUrl":"https://doi.org/arxiv-2408.13840","url":null,"abstract":"We give a new, direct proof of the tetrachotomy classification for the\u0000model-checking problem of positive equality-free logic parameterised by the\u0000model. The four complexity classes are Logspace, NP-complete, co-NP-complete\u0000and Pspace-complete. The previous proof of this result relied on notions from\u0000universal algebra and core-like structures called U-X-cores. This new proof\u0000uses only relations, and works for infinite structures also in the distinction\u0000between Logspace and NP-hard under Turing reductions. For finite domains, the membership in NP and co-NP follows from a simple\u0000argument, which breaks down already over an infinite set with a binary\u0000relation. We develop some interesting new algorithms to solve NP and co-NP\u0000membership for a variety of infinite structures. We begin with those\u0000first-order definable in (Q;=), the so-called equality languages, then move to\u0000those first-order definable in (Q;<), the so-called temporal languages.\u0000However, it is first-order expansions of the Random Graph (V,E) that provide\u0000the most interesting examples. In all of these cases, the derived\u0000classification is a tetrachotomy between Logspace, NP-complete, co-NP-complete\u0000and Pspace-complete.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192523","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":"An Overview and Comparison of Axiomatization Structures Regarding Inconsistency Indices' Properties in Pairwise Comparisons Methods","authors":"Sangeeta Pant, Anuj Kumar, Jiří Mazurek","doi":"arxiv-2408.13297","DOIUrl":"https://doi.org/arxiv-2408.13297","url":null,"abstract":"Mathematical analysis of the analytic hierarchy process (AHP) led to the\u0000development of a mathematical function, usually called the inconsistency index,\u0000which has the center role in measuring the inconsistency of the judgements in\u0000AHP. Inconsistency index is a mathematical function which maps every pairwise\u0000comparison matrix (PCM) into a real number. An inconsistency index can be\u0000considered more trustworthy when it satisfies a set of suitable properties.\u0000Therefore, the research community has been trying to postulate a set of\u0000desirable rules (axioms, properties) for inconsistency indices. Subsequently,\u0000many axiomatic frameworks for these functions have been suggested\u0000independently, however, the literature on the topic is fragmented and missing a\u0000broader framework. Therefore, the objective of this article is twofold.\u0000Firstly, we provide a comprehensive review of the advancements in the\u0000axiomatization of inconsistency indices' properties during the last decade.\u0000Secondly, we provide a comparison and discussion of the aforementioned\u0000axiomatic structures along with directions of the future research.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192527","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":"Input-based Framework for Three-valued Abstraction Refinement","authors":"Jan Onderka","doi":"arxiv-2408.12668","DOIUrl":"https://doi.org/arxiv-2408.12668","url":null,"abstract":"We present a novel algorithmic framework for Three-valued Abstraction\u0000Refinement, which extends Counterexample-guided Abstraction Refinement with the\u0000ability to verify all properties of mu-calculus including recovery (the ability\u0000of the system to always return to a certain state). The framework performs\u0000refinement on abstract system inputs rather than abstract states, avoiding\u0000problems of previous frameworks. We formalise input-based refinement by\u0000introducing the concept of generating automata, and prove that our framework is\u0000sound, monotone, and complete. We evaluate the usefulness of the framework on\u0000its implementation in our free and open-source formal verification tool.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192456","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":"The Bright Side of Timed Opacity","authors":"Étienne André, Sarah Dépernet, Engel Lefaucheux","doi":"arxiv-2408.12240","DOIUrl":"https://doi.org/arxiv-2408.12240","url":null,"abstract":"In 2009, Franck Cassez showed that the timed opacity problem, where an\u0000attacker can observe some actions with their timestamps and attempts to deduce\u0000information, is undecidable for timed automata (TAs). Moreover, he showed that\u0000the undecidability holds even for subclasses such as event-recording automata.\u0000In this article, we consider the same definition of opacity for several other\u0000subclasses of TAs: with restrictions on the number of clocks, of actions, on\u0000the nature of time, or on a new subclass called observable event-recording\u0000automata. We show that opacity can mostly be retrieved, except for one-action\u0000TAs and for one-clock TAs with epsilon-transitions, for which undecidability\u0000remains. We then exhibit a new decidable subclass in which the number of\u0000observations made by the attacker is limited.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192457","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}
Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, Nicolas Waldburger
{"title":"Invariants for One-Counter Automata with Disequality Tests","authors":"Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, Nicolas Waldburger","doi":"arxiv-2408.11908","DOIUrl":"https://doi.org/arxiv-2408.11908","url":null,"abstract":"We study the reachability problem for one-counter automata in which\u0000transitions can carry disequality tests. A disequality test is a guard that\u0000prohibits a specified counter value. This reachability problem has been known\u0000to be NP-hard and in PSPACE, and characterising its computational complexity\u0000has been left as a challenging open question by Almagor, Cohen, P'erez,\u0000Shirmohammadi, and Worrell (2020). We reduce the complexity gap, placing the\u0000problem into the second level of the polynomial hierarchy, namely into the\u0000class $mathsf{coNP}^{mathsf{NP}}$. In the presence of both equality and\u0000disequality tests, our upper bound is at the third level,\u0000$mathsf{P}^{mathsf{NP}^{mathsf{NP}}}$. To prove this result, we show that non-reachability can be witnessed by a\u0000pair of invariants (forward and backward). These invariants are almost\u0000inductive. They aim to over-approximate only a \"core\" of the reachability set\u0000instead of the entire set. The invariants are also leaky: it is possible to\u0000escape the set. We complement this with separate checks as the leaks can only\u0000occur in a controlled way.","PeriodicalId":501208,"journal":{"name":"arXiv - CS - Logic in Computer Science","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192518","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}