6 research outputs found
Extending the theory of Owicki and Gries with a logic of progress
This paper describes a logic of progress for concurrent programs. The logic
is based on that of UNITY, molded to fit a sequential programming model.
Integration of the two is achieved by using auxiliary variables in a systematic
way that incorporates program counters into the program text. The rules for
progress in UNITY are then modified to suit this new system. This modification
is however subtle enough to allow the theory of Owicki and Gries to be used
without change
Contributions of formal language theory to the study of dialogues
For more than 30 years, the problem of providing a formal framework for modeling dialogues has been a topic of great interest for the scientific areas of Linguistics, Philosophy, Cognitive Science, Formal Languages, Software Engineering and Artificial Intelligence. In the beginning the goal was to develop a "conversational computer", an automated system that could engage in a conversation in the same way as humans do. After studies showed the difficulties of achieving this goal Formal Language Theory and Artificial Intelligence have contributed to Dialogue Theory with the study and simulation of machine to machine and human to machine dialogues inspired by Linguistic studies of human interactions. The aim of our thesis is to propose a formal approach for the study of dialogues. Our work is an interdisciplinary one that connects theories and results in Dialogue Theory mainly from Formal Language Theory, but also from another areas like Artificial Intelligence, Linguistics and Multiprogramming. We contribute to Dialogue Theory by introducing a hierarchy of formal frameworks for the definition of protocols for dialogue interaction. Each framework defines a transition system in which dialogue protocols might be uniformly expressed and compared. The frameworks we propose are based on finite state transition systems and Grammar systems from Formal Language Theory and a multi-agent language for the specification of dialogue protocols from Artificial Intelligence. Grammar System Theory is a subfield of Formal Language Theory that studies how several (a finite number) of language defining devices (language processors or grammars) jointly develop a common symbolic environment (a string or a finite set of strings) by the application of language operations (for instance rewriting rules). For the frameworks we propose we study some of their formal properties, we compare their expressiveness, we investigate their practical application in Dialogue Theory and we analyze their connection with theories of human-like conversation from Linguistics. In addition we contribute to Grammar System Theory by proposing a new approach for the verification and derivation of Grammar systems. We analyze possible advantages of interpreting grammars as multiprograms that are susceptible of verification and derivation using the Owicki-Gries logic, a Hoare-based logic from the Multiprogramming field
Algebraic Principles for Program Correctness Tools in Isabelle/HOL
This thesis puts forward a flexible and principled approach to the development of
construction and verification tools for imperative programs, in which the
control flow and the data level are cleanly separated. The approach is inspired
by algebraic principles and benefits from an algebraic semantics layer.
It is programmed in the Isabelle/HOL interactive theorem prover and yields
simple lightweight mathematical components as well as program construction and
verification tools that are themselves correct by construction.
First, a simple tool is implemented using Kleeene algebra with tests (KAT)
for the control flow of while-programs, which is the most compact verification
formalism for imperative programs, and their standard relational semantics for
the data level. A reference formalisation of KAT in Isabelle/HOL is then
presented, providing three different formalisations of tests. The structured
comprehensive libraries for these algebras include an algebraic account of
Hoare logic for partial correctness. Verification condition generation and
program construction rules are based on equational reasoning and supported by
powerful Isabelle tactics and automated theorem proving.
Second, the tool is expanded to support different programming features and
verification methods. A basic program construction tool is developed by adding
an operation for the specification statement and one single axiom. To include
recursive procedures, KATs are expanded further to quantales with tests,
where iteration and the specification statement can be defined explicitly.
Additionally, a nondeterministic extension supports the verification of simple
concurrent programs.
Finally, the approach is also applied to separation logic, where the
control-flow is modelled by power series with convolution as separating
conjunction. A generic construction lifts resource monoids to assertion and
predicate transformer quantales. The data level is captured by concrete
store-heap models. These are linked to the algebra by soundness proofs.
A number of examples shows the tools at work