26 research outputs found
Marimba:A tool for verifying properties of hidden markov models
The formal verification of properties of Hidden Markov Models (HMMs) is
highly desirable for gaining confidence in the correctness of the model and the
corresponding system. A significant step towards HMM verification was the
development by Zhang et al. of a family of logics for verifying HMMs, called
POCTL*, and its model checking algorithm. As far as we know, the verification
tool we present here is the first one based on Zhang et al.'s approach. As an
example of its effective application, we verify properties of a handover task
in the context of human-robot interaction. Our tool was implemented in Haskell,
and the experimental evaluation was performed using the humanoid robot Bert2.Comment: Tool paper accepted in the 13th International Symposium on Automated
Technology for Verification and Analysis (ATVA 2015
A Component-oriented Framework for Autonomous Agents
The design of a complex system warrants a compositional methodology, i.e.,
composing simple components to obtain a larger system that exhibits their
collective behavior in a meaningful way. We propose an automaton-based paradigm
for compositional design of such systems where an action is accompanied by one
or more preferences. At run-time, these preferences provide a natural fallback
mechanism for the component, while at design-time they can be used to reason
about the behavior of the component in an uncertain physical world. Using
structures that tell us how to compose preferences and actions, we can compose
formal representations of individual components or agents to obtain a
representation of the composed system. We extend Linear Temporal Logic with two
unary connectives that reflect the compositional structure of the actions, and
show how it can be used to diagnose undesired behavior by tracing the
falsification of a specification back to one or more culpable components
Completeness and Incompleteness of Synchronous Kleene Algebra
Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was
proposed by Prisacariu as a tool for reasoning about programs that may execute
synchronously, i.e., in lock-step. We provide a countermodel witnessing that
the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a
lack of interaction between the synchronous product operator and the Kleene
star. We then propose an alternative set of axioms for SKA, based on Salomaa's
axiomatisation of regular languages, and show that these provide a sound and
complete characterisation w.r.t. the original language semantics.Comment: Accepted at MPC 201
Revisiting causality, coalgebraically
In this paper we recast the classical Darondeau–Degano’s causal semantics of concurrency in a coalgebraic setting, where we derive a compact model. Our construction is inspired by the one of Montanari and Pistore yielding causal automata, but we show that it is instance of an existing categorical framework for modeling the semantics of nominal calculi, whose relevance is further demonstrated. The key idea is to represent events as names, and
the occurrence of a new event as name generation. We model causal semantics as a coalgebra
over a presheaf, along the lines of the Fiore–Turi approach to the semantics of nominal
calculi. More specifically, we take a suitable category of finite posets, representing causal
relations over events, and we equip it with an endofunctor that allocates new events and
relates them to their causes. Presheaves over this category express the relationship between
processes and causal relations among the processes’ events. We use the allocation operator to
define a category of well-behaved coalgebras: it models the occurrence of a new event along
each transition. Then we turn the causal transition relation into a coalgebra in this category,
where labels only exhibit maximal events with respect to the source states’ poset, and we
show that its bisimilarity is essentially Darondeau–Degano’s strong causal bisimilarity. This
coalgebra is still infinite-state, but we exploit the equivalence between coalgebras over a
class of presheaves and History Dependent automata to derive a compact representation,
where states only retain the poset of the most recent events for each atomic subprocess, and
are isomorphic up to order-preserving permutations. Remarkably, this reduction of states is
automatically performed along the equivalence
Coalgebra learning via duality
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories. This allows us to learn, e.g., labelled transition systems, using Hennessy-Milner logic. Our main contribution is an abstract learning algorithm, together with a proof of correctness and termination
Soundness and completeness proofs by coinductive methods
We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOL’s recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOL’s new coinductive specification language such as nesting through non-free types and mixed recursion–corecursion
Companions, codensity and causality
In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes most enhancements and has been proved to enjoy many good properties. Here we move to universal coalgebra, where the corresponding notion is that of a final distributive law. We show that when it exists the final distributive law is a monad, and that it coincides with the codensity monad of the final sequence of the given functor. On sets, we moreover characterise this codensity monad using a new abstract notion of causality. In particular, we recover the fact that on streams, the functions definable by a distributive law or GSOS specification are precisely the causal functions. Going back to enhancements of the coinductive proof principle, we finally obtain that any causal function gives rise to a valid up-to-context technique
A Decision Procedure for (Co)datatypes in SMT Solvers
International audienceWe present a decision procedure that combines reasoning about datatypes and codatatypes. The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. The procedure decides universal problems and is composable via the Nelson–Oppen method. It has been implemented in CVC4, a state-of-the-art SMT solver. An evaluation based on problems generated from theories developed with Isabelle demonstrates the potential of the procedure
Friends with benefits: implementing corecursion in foundational proof assistants
We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference
Self-adaptive Traits in Collective Adaptive Systems
Abstract. An adaptive system is currently on spot: collective adap-tive system (CAS), which is inspired by the socio-technical systems. In CASs, highest degree of adaptation is self-adaptation consisting of self-adaptive traits. The overarching goal of CAS is to realize systems that are tightly entangled with humans and social structures. Meeting this grand challenge of CASs requires a fundamental approach to the notion of self-adaptive trait. To this end, taking advantage of the coinductive approach we construct self-adaptation monoid to shape series of self-adaptive traits in CASs and some significant relations