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Healthiness from Duality [article]

Wataru Hino, Hiroki Kobayashi, Ichiro Hasuo, Bart Jacobs
2016 arXiv   pre-print
Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for
more » ... gating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.
arXiv:1605.00381v1 fatcat:xj45obcdujg2ph6ljwdeprqgsy

Model-bounded monitoring of hybrid systems [article]

Masaki Waga, Étienne André, Ichiro Hasuo
2021 arXiv   pre-print
Monitoring of hybrid systems attracts both scientific and practical attention. However, monitoring algorithms suffer from the methodological difficulty of only observing sampled discrete-time signals, while real behaviors are continuous-time signals. To mitigate this problem of sampling uncertainties, we introduce a model-bounded monitoring scheme, where we use prior knowledge about the target system to prune interpolation candidates. Technically, we express such prior knowledge by linear
more » ... automata (LHAs) - the LHAs are called bounding models. We introduce a novel notion of monitored language of LHAs, and we reduce the monitoring problem to the membership problem of the monitored language. We present two partial algorithms - one is via reduction to reachability in LHAs and the other is a direct one using polyhedra - and show that these methods, and thus the proposed model-bounded monitoring scheme, are efficient and practically relevant.
arXiv:2102.07401v1 fatcat:espni7i5wrhojhjqlak2ntn5o4

Categorical Liveness Checking by Corecursive Algebras [article]

Natsuki Urabe, Masaki Hara, Ichiro Hasuo
2017 arXiv   pre-print
The authors are supported by ER-ATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST, and Grants-in-Aid No. 15KT0012 & 15K11984, JSPS.  ... 
arXiv:1704.04872v1 fatcat:avx7wmyhajhslpwnwxlrvyp2cq

Metamathematics for Systems Design

Ichiro Hasuo
2017 New generation computing  
This work is supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), Japan Science and Technology Agency.  ...  It is in this context that the author was awarded an ERATO grant from Japan Science and Technology Agency (JST), leading to the commencement of ERATO HASUO Metamathematics for Systems Design Project (ERATO  ... 
doi:10.1007/s00354-017-0023-1 fatcat:pw6byl77njf2boltl4qbjdh3ba

The Geometry of Synchronization (Long Version) [article]

Ugo Dal Lago, Claudia Faggian, Ichiro Hasuo, Akira Yoshimizu
2014 arXiv   pre-print
We graft synchronization onto Girard's Geometry of Interaction in its most concrete form, namely token machines. This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct modeling synchronization points, and of a multi-token abstract machine model for it. Interestingly, the correctness criterion ensures the absence of deadlocks along reduction and in the underlying machine, this way linking logical and operational properties.
arXiv:1405.3427v1 fatcat:prh5av4u55hvravxml7cocgmfq

Hyperstream processing systems

Kohei Suenaga, Hiroyoshi Sekine, Ichiro Hasuo
2013 SIGPLAN notices  
We exploit the apparent similarity between (discrete-time) stream processing and (continuous-time) signal processing and transfer a deductive verification framework from the former to the latter. Our development is based on rigorous semantics that relies on nonstandard analysis (NSA). Specifically, we start with a discrete framework consisting of a Lustre-like stream processing language, its Kahn-style fixed point semantics, and a program logic (in the form of a type system) for partial
more » ... ess guarantees. This stream framework is transferred as it is to one for hyperstreams-streams of streams, that typically arise from sampling (continuous-time) signals with progressively smaller intervals-via the logical infrastructure of NSA. Under a certain continuity assumption we identify hyperstreams with signals; our final outcome thus obtained is a deductive verification framework of signals. In it one verifies properties of signals using the (conventionally discrete) proof principles, like fixed point induction.
doi:10.1145/2480359.2429120 fatcat:tmeepx4tcjebbna7r35k7rx35a

Generic Forward and Backward Simulations [chapter]

Ichiro Hasuo
2006 Lecture Notes in Computer Science  
The technique of forward/backward simulations has been applied successfuly in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations. It is meant to be a generic version of the study by Lynch and
more » ... , covering both non-deterministic and probabilistic systems. In particular we prove soundness and completeness results with respect to trace inclusion: the proof is by coinduction using the generic theory of traces developed by Jacobs, Sokolova and the author. By suitably instantiating our generic framework, one obtains the appropriate definition of forward/backward simulations for various kinds of systems, for which soundness and completeness come for free.
doi:10.1007/11817949_27 fatcat:5xzokv4wbzgupngnqni2uzl36m

Quantitative bisimulations using coreflections and open morphisms [article]

Jérémy Dubut, Ichiro Hasuo, Shin-ya Katsumata, David Sprunger
2018 arXiv   pre-print
We investigate a canonical way of defining bisimilarity of systems when their semantics is given by a coreflection, typically in a category of transition systems. We use the fact, from Joyal et al., that coreflections preserve open morphisms situations in the sense that a coreflection induces a path subcategory in the category of systems in such a way that open bisimilarity with respect to the induced path category coincides with usual bisimilarity of their semantics. We prove that this method
more » ... s particularly well-suited for systems with quantitative information: we canonically recover the path category of probabilistic systems from Cheng et al., and of timed systems from Nielsen et al., and, finally, we propose a new canonical path category for hybrid systems.
arXiv:1809.09278v1 fatcat:47n4uw6ozfeeffhci47ydoxk6m

Semantics of Higher-Order Quantum Computation via Geometry of Interaction [article]

Ichiro Hasuo, Naohiko Hoshino
2016 arXiv   pre-print
While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work contributes to the semantical study of such languages by providing interaction-based semantics of a functional quantum programming language; the latter is, much like Selinger and Valiron's, based on linear lambda calculus and equipped with features like the !
more » ... ty and recursion. The proposed denotational model is the first one that supports the full features of a quantum functional programming language; we prove adequacy of our semantics. The construction of our model is by a series of existing techniques taken from the semantics of classical computation as well as from process theory. The most notable among them is Girard's Geometry of Interaction (GoI), categorically formulated by Abramsky, Haghverdi and Scott. The mathematical genericity of these techniques---largely due to their categorical formulation---is exploited for our move from classical to quantum.
arXiv:1605.05079v1 fatcat:xwlvnvpmajejjbkzx66ykogvfa

Coalgebraic Trace Semantics for Buechi and Parity Automata [article]

Natsuki Urabe and Shunsuke Shimizu and Ichiro Hasuo
2016 arXiv   pre-print
Schloss Dagstuhl, 2015. doi:10.4230/LIPIcs.CALCO.2015.320. 30 Natsuki Urabe and Ichiro Hasuo. Quantitative simulations by matrices. Inf. & Comp., 2016.  ...  Springer, 2002. doi:10.1007/3-540-36387-4. 15 Ichiro Hasuo, Bart Jacobs, and Ana Sokolova. Generic trace semantics via coinduction. Bart Jacobs. Trace semantics for coalgebras. Electr.  ... 
arXiv:1606.09399v1 fatcat:4edgups4mvbqjnfbeoaddeuwhe

Probabilistic Anonymity Via Coalgebraic Simulations [chapter]

Ichiro Hasuo, Yoshinobu Kawabe
2007 Lecture Notes in Computer Science  
For the jump from non-determinism to probability we fully exploit a generic, coalgebraic theory of traces and simulations developed by Hasuo and others.  ...  For the jump from non-determinism to probability we exploit a generic, coalgebraic theory of traces and simulations developed by Hasuo, Jacobs and Sokolova [9, 10] .  ... 
doi:10.1007/978-3-540-71316-6_26 fatcat:klcrpvq3krhqznu7sbed7ju3ia

Categorical Buechi and Parity Conditions via Alternating Fixed Points of Functors [article]

Natsuki Urabe, Ichiro Hasuo
2018 arXiv   pre-print
The authors are supported by JST ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), and  ... 
arXiv:1803.06811v1 fatcat:nyk3ksse3vcxnnnweavjywhjvi

Symbolic Monitoring against Specifications Parametric in Time and Data [article]

Masaki Waga and Étienne André and Ichiro Hasuo
2019 arXiv   pre-print
Monitoring consists in deciding whether a log meets a given specification. In this work, we propose an automata-based formalism to monitor logs in the form of actions associated with time stamps and arbitrarily data values over infinite domains. Our formalism uses both timing parameters and data parameters, and is able to output answers symbolic in these parameters and in the log segments where the property is satisfied or violated. We implemented our approach in an ad-hoc prototype SyMon, and
more » ... xperiments show that its high expressive power still allows for efficient online monitoring.
arXiv:1905.04486v1 fatcat:cs7rla3itrh2pmkf6gcklzeruq

Exemplifying parametric timed specifications over signals with bounded behavior [article]

Étienne André, Masaki Waga, Natsuki Urabe, Ichiro Hasuo
2022 arXiv   pre-print
This work is partially supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST and by the ANR-NRF French-Singaporean research program ProMiS (ANR-19-CE25-0015).  ... 
arXiv:2203.13247v1 fatcat:6cy4n6rfsjcd3dmxrtnew7wq4i

Traces for coalgebraic components

2011 Mathematical Structures in Computer Science  
Hasuo and B. Jacobs 4 means that the canonical maps: are isomorphisms. Additionally, the canonical map 0 → X ⊗ 0 is an isomorphism; this is the nullary case of distributivity.  ...  ; Hasuo et al., 2009) .  ...  They can be described as Cat-valued distributors/profunctors/arrows, as shown in (Hasuo et al., 2008; Hasuo et al., 2009; Asada and Hasuo, 2010) .  ... 
doi:10.1017/s0960129510000551 fatcat:ia27437lhbhu7pmbm5f2icd6ee
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