12 research outputs found
True Concurrency Can Be Easy
Net bisimilarity is a behavioral equivalence for finite Petri nets, which is
equivalent to structure-preserving bisimilarity and causal-net bisimilarity,
but with a much simpler definition, which is a smooth generalization of the
definition of standard bisimilarity on Labeled Transition Systems. We show that
it can be characterized logically by means of a suitable modal logic, called
NML (acronym of net modal logic): two markings are net bisimilar if and only if
they satisfy the same NML formulae
Unique Solutions of Contractions, CCS, and their HOL Formalisation
The unique solution of contractions is a proof technique for bisimilarity
that overcomes certain syntactic constraints of Milner's "unique solution of
equations" technique. The paper presents an overview of a rather comprehensive
formalisation of the core of the theory of CCS in the HOL theorem prover
(HOL4), with a focus towards the theory of unique solutions of contractions.
(The formalisation consists of about 20,000 lines of proof scripts in Standard
ML.) Some refinements of the theory itself are obtained. In particular we
remove the constraints on summation, which must be weakly-guarded, by moving to
rooted contraction, that is, the coarsest precongruence contained in the
contraction preorder.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807
Distributed Non-Interference
Information flow security properties were defined some years ago (see, e.g.,
the surveys \cite{FG01,Ry01}) in terms of suitable equivalence checking
problems. These definitions were provided by using sequential models of
computations (e.g., labeled transition systems \cite{GV15}), and interleaving
behavioral equivalences (e.g., bisimulation equivalence \cite{Mil89}). More
recently, the distributed model of Petri nets has been used to study
non-interference in \cite{BG03,BG09,BC15}, but also in these papers an
interleaving semantics was used. We argue that in order to capture all the
relevant information flows, truly-concurrent behavioral equivalences must be
used. In particular, we propose for Petri nets the distributed non-interference
property, called DNI, based on {\em branching place bisimilarity}
\cite{Gor21b}, which is a sensible, decidable equivalence for finite Petri nets
with silent moves. Then we focus our attention on the subclass of Petri nets
called {\em finite-state machines}, which can be represented (up to
isomorphism) by the simple process algebra CFM \cite{Gor17}. DNI is very easily
checkable on CFM processes, as it is compositional, so that it does does not
suffer from the state-space explosion problem. Moreover, we show that DNI can
be characterized syntactically on CFM by means of a type system
A Constraint-based Language for Multiparty Interactions.
Abstract Multiparty interactions are common place in today's distributed systems. An agent usually communicates, in a single session, with other agents to accomplish a given task. Take for instance an online transaction including the vendor, the client, the credit card system and the bank. When specifying this kind of system, we probably observe a single transaction including several (binary) communications leading to changes in the state of all the involved agents. Multiway synchronization process calculi, that move from a binary to a multiparty synchronization discipline, have been proposed to formally study the behavior of those systems. However, adopting models such as Bodei, Brodo, and Bruni's Core Network Algebra (CNA), where the number of participants in an interaction is not fixed a priori, leads to an exponential blow-up in the number of states/behaviors that can be observed from the system. In this paper we explore mechanisms to tackle this problem. We extend CNA with constraints that declaratively allow the modeler to restrict the interaction that should actually happen. Our extended process algebra, called CCNA, finds application in balancing the interactions in a concurrent system, leading to a simple, deadlock-free and fair solution for the Dinning Philosopher problem. Our definition of constraints is general enough and it offers the possibility of accumulating costs in a multiparty negotiation. Hence, only computations respecting the thresholds imposed by the modeler are observed. We use this machinery to neatly model a Service Level Agreement protocol. We develop the theory of CCNA including its operational semantics and a behavioral equivalence that we prove to be a congruence. We also propose a prototypical implementation that allows us to verify, automatically, some of the systems explored in the paper
Branching Place Bisimilarity
Place bisimilarity is a behavioral equivalence for finite Petri nets,
proposed in \cite{ABS91} and proved decidable in \cite{Gor21}. In this paper we
propose an extension to finite Petri nets with silent moves of the place
bisimulation idea, yielding {\em branching} place bisimilarity ,
following the intuition of branching bisimilarity \cite{vGW96} on labeled
transition systems. We also propose a slightly coarser variant, called
branching {\em d-place} bisimilarity , following the intuition of
d-place bisimilarity in \cite{Gor21}. We prove that and
are decidable equivalence relations. Moreover, we prove that is
strictly finer than branching fully-concurrent bisimilarity
\cite{Pin93,Gor20c}, essentially because does not consider as
unobservable those -labeled net transitions with pre-set size larger than
one, i.e., those resulting from (multi-party) interaction.Comment: arXiv admin note: text overlap with arXiv:2104.01392,
arXiv:2104.1485
Compositional Semantics of Finite Petri Nets
Structure-preserving bisimilarity is a truly concurrent behavioral
equivalence for finite Petri nets, which relates markings (of the same size
only) generating the same causal nets, hence also the same partial orders of
events. The process algebra FNM truly represents all (and only) the finite
Petri nets, up to isomorphism. We prove that structure-preserving bisimilarity
is a congruence w.r.t. the FMN operators, In this way, we have defined a
compositional semantics, fully respecting causality and the branching structure
of systems, for the class of all the finite Petri nets. Moreover, we study some
algebraic properties of structure-preserving bisimilarity, that are at the base
of a sound (but incomplete) axiomatization over FNM process terms.Comment: arXiv admin note: substantial text overlap with arXiv:2301.0448
Monotone Precision and Recall Measures for Comparing Executions and Specifications of Dynamic Systems
The behavioural comparison of systems is an important concern of software
engineering research. For example, the areas of specification discovery and
specification mining are concerned with measuring the consistency between a
collection of execution traces and a program specification. This problem is
also tackled in process mining with the help of measures that describe the
quality of a process specification automatically discovered from execution
logs. Though various measures have been proposed, it was recently demonstrated
that they neither fulfil essential properties, such as monotonicity, nor can
they handle infinite behaviour. In this paper, we address this research problem
by introducing a new framework for the definition of behavioural quotients. We
proof that corresponding quotients guarantee desired properties that existing
measures have failed to support. We demonstrate the application of the
quotients for capturing precision and recall measures between a collection of
recorded executions and a system specification. We use a prototypical
implementation of these measures to contrast their monotonic assessment with
measures that have been defined in prior research