30 research outputs found
Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma
Dickson's Lemma is a simple yet powerful tool widely used in termination
proofs, especially when dealing with counters or related data structures.
However, most computer scientists do not know how to derive complexity upper
bounds from such termination proofs, and the existing literature is not very
helpful in these matters.
We propose a new analysis of the length of bad sequences over (N^k,\leq) and
explain how one may derive complexity upper bounds from termination proofs. Our
upper bounds improve earlier results and are essentially tight
Verifying temporal properties of systems with applications to petri nets
This thesis provides a powerful general-purpose proof technique for the verification
of systems, whether finite or infinite. It extends the idea of finite local
model-checking, which was introduced by Stirling and Walker: rather than
traversing the entire state space of a model, as is done for model-checking in
the sense of Emerson, Clarke et al. (checking whether a (finite) model satisfies
a formula), local model-checking asks whether a particular state satisfies a formula,
and only explores the nearby states far enough to answer that question.
The technique used was a tableau method, constructing a tableau according to
the formula and the local structure of the model. This tableau technique is here
generalized to the infinite case by considering sets of states, rather than single
states; because the logic used, the propositional modal mu-calculus, separates
simple modal and boolean connectives from powerful fix-point operators (which
make the logic more expressive than many other temporal logics), it is possible
to give a relatively straightforward set of rules for constructing a tableau. Much
of the subtlety is removed from the tableau itself, and put into a relation on the
state space defined by the tableau-the success of the tableau then depends on
the well-foundedness of this relation.
This development occupies the second and third chapters: the second considers
the modal mu-calculus, and explains its power, while the third develops
the tableau technique itself
The generalized tableau technique is exhibited on Petri nets, and various
standard notions from net theory are shown to play a part in the use of the
technique on nets-in particular, the invariant calculus has a major role.
The requirement for a finite presentation of tableaux for infinite systems
raises the question of the expressive power of the mu-calculus. This is studied in
some detail, and it is shown that on reasonably powerful models of computation,
such as Petri nets, the mu-calculus can express properties that are not merely
undecidable, but not even arithmetical.
The concluding chapter discusses some of the many questions still to be
answered, such as the incorporation of formal reasoning within the tableau
system, and the power required of such reasoning
Transforming structures by set interpretations
We consider a new kind of interpretation over relational structures: finite
sets interpretations. Those interpretations are defined by weak monadic
second-order (WMSO) formulas with free set variables. They transform a given
structure into a structure with a domain consisting of finite sets of elements
of the orignal structure. The definition of these interpretations directly
implies that they send structures with a decidable WMSO theory to structures
with a decidable first-order theory. In this paper, we investigate the
expressive power of such interpretations applied to infinite deterministic
trees. The results can be used in the study of automatic and tree-automatic
structures.Comment: 36 page
On Reasoning about Infinite-State Systems in the Modal µ-Calculus
This paper presents a proof method for proving that infinite-state systems satisfy properties expressed in the modal µ-calculus. The method is sound and complete relative to externally proving inclusions of sets of states. It can be seen as a recast of a tableau method due to Bradfield and Stirling following lines used by Winskel for finite-state systems. Contrary to the tableau method, it avoids the use of constants when unfolding fixed points and it replaces the rather involved global success criterion in the tableau method with local success criteria. A proof tree is now merely a means of keeping track of where possible choices are made -- and can be changed -- and not an essential ingredient in establishing the correctness of a proof: A proof will be correct when all leaves can be directly seen to be valid. Therefore, it seems well-suited for implementation as a tool, by, for instance, integration into existing general-purpose theorem provers
Events in computation
SIGLEAvailable from British Library Document Supply Centre- DSC:D36018/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
On the expressiveness of higher dimensional automata
In this paper I compare the expressive power of several models of concurrency based on their ability to represent causal dependence. To this end, I translate these models, in behaviour preserving ways, into the model of higher dimensional automata (HDA), which is the most expressive model under investigation. In particular, I propose four different translations of Petri nets, corresponding to the four different computational interpretations of nets found in the literature. I also extend various equivalence relations for concurrent systems to HDA. These include the history preserving bisimulation, which is the coarsest equivalence that fully respects branching time, causality and their interplay, as well as the ST-bisimulation, a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time. Through their embeddings in HDA, it is now well-defined whether members of different models of concurrency are equivalent. (c) 2006 Elsevier B.V. All rights reserved
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.