14 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Span(Graph): a Canonical Feedback Algebra of Open Transition Systems
We show that Span(Graph)*, an algebra for open transition systems introduced
by Katis, Sabadini and Walters, satisfies a universal property. By itself, this
is a justification of the canonicity of this model of concurrency. However, the
universal property is itself of interest, being a formal demonstration of the
relationship between feedback and state. Indeed, feedback categories, also
originally proposed by Katis, Sabadini and Walters, are a weakening of traced
monoidal categories, with various applications in computer science. A state
bootstrapping technique, which has appeared in several different contexts,
yields free such categories. We show that Span(Graph)* arises in this way,
being the free feedback category over Span(Set). Given that the latter can be
seen as an algebra of predicates, the algebra of open transition systems thus
arises - roughly speaking - as the result of bootstrapping state to that
algebra. Finally, we generalize feedback categories endowing state spaces with
extra structure: this extends the framework from mere transition systems to
automata with initial and final states.Comment: 48 pages, 33 figures, journal versio
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
Relating Apartness and Bisimulation
A bisimulation for a coalgebra of a functor on the category of sets can be
described via a coalgebra in the category of relations, of a lifted functor. A
final coalgebra then gives rise to the coinduction principle, which states that
two bisimilar elements are equal. For polynomial functors, this leads to
well-known descriptions. In the present paper we look at the dual notion of
"apartness". Intuitively, two elements are apart if there is a positive way to
distinguish them. Phrased differently: two elements are apart if and only if
they are not bisimilar. Since apartness is an inductive notion, described by a
least fixed point, we can give a proof system, to derive that two elements are
apart. This proof system has derivation rules and two elements are apart if and
only if there is a finite derivation (using the rules) of this fact.
We study apartness versus bisimulation in two separate ways. First, for weak
forms of bisimulation on labelled transition systems, where silent (tau) steps
are included, we define an apartness notion that corresponds to weak
bisimulation and another apartness that corresponds to branching bisimulation.
The rules for apartness can be used to show that two states of a labelled
transition system are not branching bismilar. To support the apartness view on
labelled transition systems, we cast a number of well-known properties of
branching bisimulation in terms of branching apartness and prove them. Next, we
also study the more general categorical situation and show that indeed,
apartness is the dual of bisimilarity in a precise categorical sense: apartness
is an initial algebra and gives rise to an induction principle. In this
analogy, we include the powerset functor, which gives a semantics to
non-deterministic choice in process-theory
Control-Data Separation and Logical Condition Propagation for Efficient Inference on Probabilistic Programs
We introduce a novel sampling algorithm for Bayesian inference on imperative
probabilistic programs. It features a hierarchical architecture that separates
control flows from data: the top-level samples a control flow, and the bottom
level samples data values along the control flow picked by the top level. This
separation allows us to plug various language-based analysis techniques in
probabilistic program sampling; specifically, we use logical backward
propagation of observations for sampling efficiency. We implemented our
algorithm on top of Anglican. The experimental results demonstrate our
algorithm's efficiency, especially for programs with while loops and rare
observations.Comment: 11 pages with appendice
Coalgebraic Geometric Logic: Basic Theory
Using the theory of coalgebra, we introduce a uniform framework for adding
modalities to the language of propositional geometric logic. Models for this
logic are based on coalgebras for an endofunctor on some full subcategory of
the category of topological spaces and continuous functions. We investigate
derivation systems, soundness and completeness for such geometric modal logics,
and we we specify a method of lifting an endofunctor on Set, accompanied by a
collection of predicate liftings, to an endofunctor on the category of
topological spaces, again accompanied by a collection of (open) predicate
liftings. Furthermore, we compare the notions of modal equivalence, behavioural
equivalence and bisimulation on the resulting class of models, and we provide a
final object for the corresponding category
A small-step approach to multi-trace checking against interactions
Interaction models describe the exchange of messages between the different
components of distributed systems. We have previously defined a small-step
operational semantics for interaction models. The paper extends this work by
presenting an approach for checking the validity of multi-traces against
interaction models. A multi-trace is a collection of traces (sequences of
emissions and receptions), each representing a local view of the same global
execution of the distributed system. We have formally proven our approach,
studied its complexity, and implemented it in a prototype tool. Finally, we
discuss some observability issues when testing distributed systems via the
analysis of multi-traces.Comment: long version - 26 pages (23 for paper, 2 for bibliography, and a 1
page annex) - 15 figures (1 in annex
Expressive Logics for Coinductive Predicates
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata