arXiv subjects

Ichiro Hasuo

Publications and source records attributed to Ichiro Hasuo.

At least 73 records · Page 4Linked to original sources

arXiv2018

Fast Falsification of Hybrid Systems using Probabilistically Adaptive Input

We present an algorithm that quickly finds falsifying inputs for hybrid systems, i.e., inputs that steer the system towards violation of a given temporal logic requirement. Our method is based on a probabilistically directed search of an increasingly fine grained spatial and temporal discretization of the input space. A key feature is that it adapts to the difficulty of a problem at hand, specifically to the local complexity of each input segment, as needed for falsification. In experiments with standard benchmarks, our approach consistently outperforms existing techniques by a significant margin. In recognition of the way it works and to distinguish it from previous work, we describe our method as a "Las Vegas tree search".

eess.SY↗

arXiv2018

Quantitative Simulations by Matrices

We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language inclusion comes for free---but are concretely presented as matrices that are subject to linear inequality constraints. Pervasiveness of these formalisms allows us to exploit existing algorithms in: searching for a simulation, and hence verifying quantitative correctness that is formulated as language inclusion. Transformations of automata that aid search for simulations are introduced, too. This verification workflow is implemented for the plus-times and max-plus semirings. Furthermore, an extension to weighted tree automata is presented and implemented.

cs.LO↗

arXiv2018

MONAA: A Tool for Timed Pattern Matching with Automata-Based Acceleration

We present monaa, a monitoring tool over a real-time property specified by either a timed automaton or a timed regular expression. It implements a timed pattern matching algorithm that combines 1) features suited for online monitoring, and 2) acceleration by automata-based skipping. Our experiments demonstrate monaa's performance advantage, especially in online usage.

cs.FL↗

arXiv2018

Quantitative bisimulations using coreflections and open morphisms

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 is 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.

cs.LO↗

arXiv2018

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs

Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities. Based on the existing works that stretch across different communities (formal verification, control theory, etc.), we offer a unifying account. In particular, we emphasize the role of order-theoretic fixed points---a classic topic in computer science---in the analysis of probabilistic programs. This leads us to two new martingale-based techniques, too. We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.

cs.PL↗

arXiv2018

Coalgebraic Infinite Traces and Kleisli Simulations

Kleisli simulation is a categorical notion introduced by Hasuo to verify finite trace inclusion. They allow us to give definitions of forward and backward simulation for various types of systems. A generic categorical theory behind Kleisli simulation has been developed and it guarantees the soundness of those simulations with respect to finite trace semantics. Moreover, those simulations can be aided by forward partial execution (FPE)---a categorical transformation of systems previously introduced by the authors. In this paper, we give Kleisli simulation a theoretical foundation that assures its soundness also with respect to infinitary traces. There, following Jacobs' work, infinitary trace semantics is characterized as the "largest homomorphism." It turns out that soundness of forward simulations is rather straightforward; that of backward simulation holds too, although it requires certain additional conditions and its proof is more involved. We also show that FPE can be successfully employed in the infinitary trace setting to enhance the applicability of Kleisli simulations as witnesses of trace inclusion. Our framework is parameterized in the monad for branching as well as in the functor for linear-time behaviors; for the former we mainly use the powerset monad (for nondeterminism), the sub-Giry monad (for probability), and the lift monad (for exception).

cs.LO↗

arXiv2018

Two-Layered Falsification of Hybrid Systems guided by Monte Carlo Tree Search

Few real-world hybrid systems are amenable to formal verification, due to their complexity and black box components. Optimization-based falsification---a methodology of search-based testing that employs stochastic optimization---is attracting attention as an alternative quality assurance method. Inspired by the recent works that advocate coverage and exploration in falsification, we introduce a two-layered optimization framework that uses Monte Carlo tree search (MCTS), a popular machine learning technique with solid mathematical and empirical foundations. MCTS is used in the upper layer of our framework; it guides the lower layer of local hill-climbing optimization, thus balancing exploration and exploitation in a disciplined manner.

eess.SY↗

arXiv2018

Categorical Buechi and Parity Conditions via Alternating Fixed Points of Functors

Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens. We formalize notions of alternating fixed points of functors using constructions that are similar to that of free monads. We find their use in categorical modeling of accepting run trees under the Buechi and parity acceptance condition. This modeling abstracts away from states of an automaton; it can thus be thought of as the "behaviors" of systems with the Buechi or parity conditions, in a way that follows the tradition of coalgebraic modeling of system behaviors.

cs.LO↗

arXiv2017

Bounding Errors Due to Switching Delays in Incrementally Stable Switched Systems (Extended Version)

Time delays pose an important challenge in networked control systems, which are now ubiquitous. Focusing on switched systems, we introduce a framework that provides an upper bound for errors caused by switching delays. Our framework is based on approximate bisimulation, a notion that has been previously utilized mainly for symbolic (discrete) abstraction of state spaces. Notable in our framework is that, in deriving an approximate bisimulation and thus an error bound, we use a simple incremental stability assumption (namely δ-GUAS) that does not itself refer to time delays. That this is the same assumption used for state-space discretization enables a two-step workflow for control synthesis for switched systems, in which a single Lyapunov-type stability witness serves for two different purposes of state discretization and coping with time delays. We demonstrate the proposed framework with a boost DC-DC converter, a common example of switched systems.

eess.SY↗

arXiv2017

Causality-Aided Falsification

Falsification is drawing attention in quality assurance of heterogeneous systems whose complexities are beyond most verification techniques' scalability. In this paper we introduce the idea of causality aid in falsification: by providing a falsification solver -- that relies on stochastic optimization of a certain cost function -- with suitable causal information expressed by a Bayesian network, search for a falsifying input value can be efficient. Our experiment results show the idea's viability.

eess.SY↗

arXiv2017

Fair Simulation for Nondeterministic and Probabilistic Buechi Automata: a Coalgebraic Perspective

Notions of simulation, among other uses, provide a computationally tractable and sound (but not necessarily complete) proof method for language inclusion. They have been comprehensively studied by Lynch and Vaandrager for nondeterministic and timed systems; for Büchi automata the notion of fair simulation has been introduced by Henzinger, Kupferman and Rajamani. We contribute to a generalization of fair simulation in two different directions: one for nondeterministic tree automata previously studied by Bomhard; and the other for probabilistic word automata with finite state spaces, both under the Büchi acceptance condition. The former nondeterministic definition is formulated in terms of systems of fixed-point equations, hence is readily translated to parity games and is then amenable to Jurdziński's algorithm; the latter probabilistic definition bears a strong ranking-function flavor. These two different-looking definitions are derived from one source, namely our coalgebraic modeling of Büchi automata. Based on these coalgebraic observations, we also prove their soundness: a simulation indeed witnesses language inclusion.

cs.LO↗

arXiv2017

Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples.

cs.LO↗

arXiv2017

Efficient Online Timed Pattern Matching by Automata-Based Skipping

The timed pattern matching problem is an actively studied topic because of its relevance in monitoring of real-time systems. There one is given a log $w$ and a specification $\mathcal{A}$ (given by a timed word and a timed automaton in this paper), and one wishes to return the set of intervals for which the log $w$, when restricted to the interval, satisfies the specification $\mathcal{A}$. In our previous work we presented an efficient timed pattern matching algorithm: it adopts a skipping mechanism inspired by the classic Boyer--Moore (BM) string matching algorithm. In this work we tackle the problem of online timed pattern matching, towards embedded applications where it is vital to process a vast amount of incoming data in a timely manner. Specifically, we start with the Franek-Jennings-Smyth (FJS) string matching algorithm---a recent variant of the BM algorithm---and extend it to timed pattern matching. Our experiments indicate the efficiency of our FJS-type algorithm in online and offline timed pattern matching.

cs.FL↗

arXiv2017

Categorical Liveness Checking by Corecursive Algebras

Final coalgebras as "categorical greatest fixed points" play a central role in the theory of coalgebras. Somewhat analogously, most proof methods studied therein have focused on greatest fixed-point properties like safety and bisimilarity. Here we make a step towards categorical proof methods for least fixed-point properties over dynamical systems modeled as coalgebras. Concretely, we seek a categorical axiomatization of well-known proof methods for liveness, namely ranking functions (in nondeterministic settings) and ranking supermartingales (in probabilistic ones). We find an answer in a suitable combination of coalgebraic simulation (studied previously by the authors) and corecursive algebra as a classifier for (non-)well-foundedness.

cs.LO↗

arXiv2016

Coalgebraic Trace Semantics for Buechi and Parity Automata

Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the theory of automata for infinite words or trees. In this paper we present a clean answer to the question that builds on the "maximality" characterization of infinite traces (by Jacobs and Cirstea): the accepted language of a Buechi automaton is characterized by two commuting diagrams, one for a least homomorphism and the other for a greatest, much like in a system of (least and greatest) fixed-point equations. This characterization works uniformly for the nondeterministic branching and the probabilistic one; and for words and trees alike. We present our results in terms of the parity acceptance condition that generalizes Buechi's.

cs.LO↗

arXiv2016

A Boyer-Moore Type Algorithm for Timed Pattern Matching

The timed pattern matching problem is formulated by Ulus et al. and has been actively studied since, with its evident application in monitoring real-time systems. The problem takes as input a timed word/signal and a timed pattern (specified either by a timed regular expression or by a timed automaton); and it returns the set of those intervals for which the given timed word, when restricted to the interval, matches the given pattern. We contribute a Boyer-Moore type optimization in timed pattern matching, relying on the classic Boyer-Moore string matching algorithm and its extension to (untimed) pattern matching by Watson and Watson. We assess its effect through experiments; for some problem instances our Boyer-Moore type optimization achieves speed-up by two times, indicating its potential in real-world monitoring tasks where data sets tend to be massive.

cs.FL↗

arXiv2016

Semantics of Higher-Order Quantum Computation via Geometry of Interaction

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 ! modality 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.

cs.LO↗

arXiv2016

Healthiness from Duality

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 investigating 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.

cs.LO↗