4,016 research outputs found
On Multi-Robot Path Planning Based on Petri Net Models and LTL specifications
This work considers the path planning problem for a team of identical robots
evolving in a known environment. The robots should satisfy a global
specification given as a Linear Temporal Logic (LTL) formula over a set of
regions of interest. The proposed method exploits the advantages of Petri net
models for the team of robots and B\"uchi automata modeling the specification.
The approach in this paper consists in combining the two models into one,
denoted Composed Petri net and use it to find a sequence of action movements
for the mobile robots, providing collision free trajectories to fulfill the
specification. The solution results from a set of Mixed Integer Linear
Programming (MILP) problems. The main advantage of the proposed solution is the
completeness of the algorithm, meaning that a solution is found when exists,
this representing the key difference with our previous work in [1]. The
simulations illustrate comparison results between current and previous
approaches, focusing on the computational complexity.Comment: submitted to IEEE Transactions on Automatic Control, 202
An Effective Fixpoint Semantics for Linear Logic Programs
In this paper we investigate the theoretical foundation of a new bottom-up
semantics for linear logic programs, and more precisely for the fragment of
LinLog that consists of the language LO enriched with the constant 1. We use
constraints to symbolically and finitely represent possibly infinite
collections of provable goals. We define a fixpoint semantics based on a new
operator in the style of Tp working over constraints. An application of the
fixpoint operator can be computed algorithmically. As sufficient conditions for
termination, we show that the fixpoint computation is guaranteed to converge
for propositional LO. To our knowledge, this is the first attempt to define an
effective fixpoint semantics for linear logic programs. As an application of
our framework, we also present a formal investigation of the relations between
LO and Disjunctive Logic Programming. Using an approach based on abstract
interpretation, we show that DLP fixpoint semantics can be viewed as an
abstraction of our semantics for LO. We prove that the resulting abstraction is
correct and complete for an interesting class of LO programs encoding Petri
Nets.Comment: 39 pages, 5 figures. To appear in Theory and Practice of Logic
Programmin
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
Model Checking Linear Logic Specifications
The overall goal of this paper is to investigate the theoretical foundations
of algorithmic verification techniques for first order linear logic
specifications. The fragment of linear logic we consider in this paper is based
on the linear logic programming language called LO enriched with universally
quantified goal formulas. Although LO was originally introduced as a
theoretical foundation for extensions of logic programming languages, it can
also be viewed as a very general language to specify a wide range of
infinite-state concurrent systems.
Our approach is based on the relation between backward reachability and
provability highlighted in our previous work on propositional LO programs.
Following this line of research, we define here a general framework for the
bottom-up evaluation of first order linear logic specifications. The evaluation
procedure is based on an effective fixpoint operator working on a symbolic
representation of infinite collections of first order linear logic formulas.
The theory of well quasi-orderings can be used to provide sufficient conditions
for the termination of the evaluation of non trivial fragments of first order
linear logic.Comment: 53 pages, 12 figures "Under consideration for publication in Theory
and Practice of Logic Programming
Bounded LTL Model Checking with Stable Models
In this paper bounded model checking of asynchronous concurrent systems is
introduced as a promising application area for answer set programming. As the
model of asynchronous systems a generalisation of communicating automata,
1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a
requirement on the behaviour of the net can be translated into a logic program
such that the bounded model checking problem for the net can be solved by
computing stable models of the corresponding program. The use of the stable
model semantics leads to compact encodings of bounded reachability and deadlock
detection tasks as well as the more general problem of bounded model checking
of linear temporal logic. Correctness proofs of the devised translations are
given, and some experimental results using the translation and the Smodels
system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin
A System for Deduction-based Formal Verification of Workflow-oriented Software Models
The work concerns formal verification of workflow-oriented software models
using deductive approach. The formal correctness of a model's behaviour is
considered. Manually building logical specifications, which are considered as a
set of temporal logic formulas, seems to be the significant obstacle for an
inexperienced user when applying the deductive approach. A system, and its
architecture, for the deduction-based verification of workflow-oriented models
is proposed. The process of inference is based on the semantic tableaux method
which has some advantages when compared to traditional deduction strategies.
The algorithm for an automatic generation of logical specifications is
proposed. The generation procedure is based on the predefined workflow patterns
for BPMN, which is a standard and dominant notation for the modeling of
business processes. The main idea for the approach is to consider patterns,
defined in terms of temporal logic,as a kind of (logical) primitives which
enable the transformation of models to temporal logic formulas constituting a
logical specification. Automation of the generation process is crucial for
bridging the gap between intuitiveness of the deductive reasoning and the
difficulty of its practical application in the case when logical specifications
are built manually. This approach has gone some way towards supporting,
hopefully enhancing our understanding of, the deduction-based formal
verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc
Linear logic on Petri nets
This article shows how individual Petri nets form models of Girard's intuitionistic linear logic. It explores questions of expressiveness and completeness of linear logic with respect to this interpretation. An aim is to use Petri nets to give an understanding of linear logic and give some appraisal of the value of linear logic as a specification logic for Petri nets. This article might serve as a tutorial, providing one in-road into Girard's linear logic via Petri nets. With this in mind we have added several exercises and their solutions. We have made no attempt to be exhaustive in our treatment, dedicating our treatment to one semantics of intuitionistic linear logic. Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic, with (*), --, &, (+) and the exponential ! (``of course''), and forms of quantification. This logic is shown sound and complete with respect to atomic nets (these include nets in which every transition leads to a nonempty multiset of places). The logic is remarkably expressive, enabling descriptions of the kinds of properties one might wish to show of nets; in particular, negative properties, asserting the impossibility of an assertion, can also be expressed. A start is made on decidability issues
A Linear Logic Based Approach to Timed Petri Nets
1.1 Relationship between Petri net and linear logic Petri nets were first introduced by Petri in his seminal Ph.D. thesis, and both the theory and the applications of his model have flourished in concurrency theory (Reisig & Rozenberg, 1998a; Reisig & Rozenberg, 1998b)
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