[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84594-en":3,"doc-seo-84594-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84594,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Effective Stochastic Automata Model Checking by Interval Abstraction (Extended Version)","Stochastic automata provide a formal continuous-time model with countdown timers whose expiration follows general probability distributions, enabling faithful dependability and performance analysis for systems with faults, maintenance, and repairs. Existing effective analysis is largely confined to statistical model checking of restrictive deterministic cases. This paper introduces a general and effective SA model checking approach combining refinable interval abstraction of continuous distributions with “big time steps” semantics, yielding upper and lower bounds on reachability probabilities. A prototype implementation in Rust extends Modest and Jani with SA support.","arXiv :2607 .00782v 1 [ cs .LO] 1 Jul 2026  \nEffective Stochastic Automata Model  \nChecking by Interval Abstraction⋆  \n(extended version)  \nPedro R. D’Argenio 1 , Arnd Hartmanns2 , and Annabell Petri2 (􀀌)  \n1 Universidad Nacional de Córdoba and CONICET, Córdoba, Argentina  \n2 University of Twente, Enschede, The Netherlands · [annabell.petri@utwente.nl](annabell.petri@utwente.nl)  \nAbstract. Stochastic automata (SA) are a formal stochastic continuoustime model based on countdown timers whose expiration times follow general probability distributions. SA are particularly useful to faithfully model and analyse dependable systems involving faults, maintenance, and repairs. Effective SA analysis approaches have so far been limited to statistical model checking and thus deterministic SA, while previously proposed model-checking techniques apply to limited subclasses of SA only, or do not scale. In this paper, we present the first dedicated SA model checking approach that is general and effective: It puts few restrictions on the input SA, and we show in our experimental evaluation that it works well for nontrivial examples. It combines a refinable interval abstraction of the continuous distributions with a direct application of the “big time steps” semantics of SA, providing upper/lower boundson maximum/minimum reachability probabilities. We extend the Modest and Jani modelling formalisms with support for SA, and provide a prototype implementation of our approach in Rust.  \n1 Introduction  \nIn dependable systems, component faults happen randomly over time, with schemes involving redundancy, regular inspections, maintenance, and repairs attempting to prevent escalation into overall system failure. Similarly, in highperformance systems, random queueing and service times, message loss probabilities, and signal transmission and propagation delays determine the system’s key performance properties such as throughput or response times. Formal models for dependability and performance evaluation [4] need to capture these aspects of stochastic time in a realistic way, as close as possible to the real system or the available data. Two widely-used formalisms are continuous-time Markov chains (CTMCs) and generalized stochastic Petri nets (GSPNs) [18, 37] . In both, all delays must be exponentially distributed. The resulting memoryless nature of  \n⋆ Authors are sorted in alphabetical order. This work was supported by the EU’s H2020 R & I programme under MSCA grant agreement 101008233 (MISSION), by the Interreg North Sea project STORM_SAFE, by SeCyT-UNC grant 33620230100384CB (MECANO), and by NWO VIDI grant VI.Vidi.223.110 (TruSTy) .  \n2 P. R. D’Argenio, A. Hartmanns, A. Petri  \nthese models admits scalable analytical analysis methods such as probabilistic model checking [2,3] . In reality, however, many inter-event times are not exponentially distributed, and hard to approximate by CTMCs/phase-type distributions: time to failure is more realistically modelled by a Weibull distribution in most cases, and inspections typically happen around fixed intervals. We thus need non-Markovian formalisms that directly incorporate general continuous probability distributions, such as stochastic automata (SA) [14] or Petri nets with general transitions (e.g. HPnGs [22]) . In this paper, we use SA, because they are conceptually simple yet highly expressive. Additionally, their compositionality makes them attractive for modelling complex component-based systems.  \nSA extend labelled transition systems with stochastic timers (that may be reset to values sampled from continuous probability distributions to then decrease over time and expire when reaching value zero) and guard sets that enable an edge when all their timers have expired. As SA are non-Markovian and allow nondeterministic choices, their analysis is hard. The only available tool with dedicated SA support, Fig [9], employs statistical model checking [1, 36] (i.e. Monte Carlo simulation) and is thus restr","cbCainpK6g4gcSBk","https://ap.wps.com/l/cbCainpK6g4gcSBk","pdf",905235,1,25,"English","en",105,"# Introduction\n## Related Work\n## Interval Abstraction Approach\n## Formal Specification and Overapproximation\n## Modest and Jani Extensions\n## Prototype Implementation and Evaluation","[{\"question\":\"What makes stochastic automata (SA) suitable for dependability and performance modeling?\",\"answer\":\"SA model random failures, maintenance, repairs, queueing/service times, and delays using countdown timers whose expiration times follow general probability distributions, rather than requiring exponential delays only.\"},{\"question\":\"How does interval abstraction improve SA model checking?\",\"answer\":\"Interval abstraction replaces each continuous distribution sampling with a discrete distribution over finitely many intervals, then propagates intervals symbolically through SA semantics, producing an MDP that overapproximates the SA behavior.\"},{\"question\":\"What probabilities does the approach compute, and how are they related to the original SA?\",\"answer\":\"Using value iteration on the induced MDP, the method computes maximum and minimum probabilities of reaching goal-related states, which serve as upper and lower bounds on the corresponding reachability probabilities in the SA.\"}]",1784196990,63,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"effective-stochastic-automata-model-checking-by-interval-abstraction-extended-version","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/effective-stochastic-automata-model-checking-by-interval-abstraction-extended-version/84594/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What makes stochastic automata (SA) suitable for dependability and performance modeling?","Question",{"text":75,"@type":76},"SA model random failures, maintenance, repairs, queueing/service times, and delays using countdown timers whose expiration times follow general probability distributions, rather than requiring exponential delays only.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does interval abstraction improve SA model checking?",{"text":80,"@type":76},"Interval abstraction replaces each continuous distribution sampling with a discrete distribution over finitely many intervals, then propagates intervals symbolically through SA semantics, producing an MDP that overapproximates the SA behavior.",{"name":82,"@type":73,"acceptedAnswer":83},"What probabilities does the approach compute, and how are they related to the original SA?",{"text":84,"@type":76},"Using value iteration on the induced MDP, the method computes maximum and minimum probabilities of reaching goal-related 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