79 research outputs found
An Exercise in Invariant-based Programming with Interactive and Automatic Theorem Prover Support
Invariant-Based Programming (IBP) is a diagram-based correct-by-construction
programming methodology in which the program is structured around the
invariants, which are additionally formulated before the actual code. Socos is
a program construction and verification environment built specifically to
support IBP. The front-end to Socos is a graphical diagram editor, allowing the
programmer to construct invariant-based programs and check their correctness.
The back-end component of Socos, the program checker, computes the verification
conditions of the program and tries to prove them automatically. It uses the
theorem prover PVS and the SMT solver Yices to discharge as many of the
verification conditions as possible without user interaction. In this paper, we
first describe the Socos environment from a user and systems level perspective;
we then exemplify the IBP workflow by building a verified implementation of
heapsort in Socos. The case study highlights the role of both automatic and
interactive theorem proving in three sequential stages of the IBP workflow:
developing the background theory, formulating the program specification and
invariants, and proving the correctness of the final implementation.Comment: In Proceedings THedu'11, arXiv:1202.453
Mutual Mobile Membranes with Timers
A feature of current membrane systems is the fact that objects and membranes
are persistent. However, this is not true in the real world. In fact, cells and
intracellular proteins have a well-defined lifetime. Inspired from these
biological facts, we define a model of systems of mobile membranes in which
each membrane and each object has a timer representing their lifetime. We show
that systems of mutual mobile membranes with and without timers have the same
computational power. An encoding of timed safe mobile ambients into systems of
mutual mobile membranes with timers offers a relationship between two
formalisms used in describing biological systems
Quantifying the implicit process flow abstraction in SBGN-PD diagrams with Bio-PEPA
For a long time biologists have used visual representations of biochemical
networks to gain a quick overview of important structural properties. Recently
SBGN, the Systems Biology Graphical Notation, has been developed to standardise
the way in which such graphical maps are drawn in order to facilitate the
exchange of information. Its qualitative Process Diagrams (SBGN-PD) are based
on an implicit Process Flow Abstraction (PFA) that can also be used to
construct quantitative representations, which can be used for automated
analyses of the system. Here we explicitly describe the PFA that underpins
SBGN-PD and define attributes for SBGN-PD glyphs that make it possible to
capture the quantitative details of a biochemical reaction network. We
implemented SBGNtext2BioPEPA, a tool that demonstrates how such quantitative
details can be used to automatically generate working Bio-PEPA code from a
textual representation of SBGN-PD that we developed. Bio-PEPA is a process
algebra that was designed for implementing quantitative models of concurrent
biochemical reaction systems. We use this approach to compute the expected
delay between input and output using deterministic and stochastic simulations
of the MAPK signal transduction cascade. The scheme developed here is general
and can be easily adapted to other output formalisms
On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems
Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed. Mathematical modeling of
biological systems with delays is usually based on Delay Differential Equations
(DDEs), a kind of differential equations in which the derivative of the unknown
function at a certain time is given in terms of the values of the function at
previous times. In the literature, delay stochastic simulation algorithms have
been proposed. These algorithms follow a "delay as duration" approach, namely
they are based on an interpretation of a delay as the elapsing time between the
start and the termination of a chemical reaction. This interpretation is not
suitable for some classes of biological systems in which species involved in a
delayed interaction can be involved at the same time in other interactions. We
show on a DDE model of tumor growth that the delay as duration approach for
stochastic simulation is not precise, and we propose a simulation algorithm
based on a ``purely delayed'' interpretation of delays which provides better
results on the considered model
Automated Generation of User Guidance by Combining Computation and Deduction
Herewith, a fairly old concept is published for the first time and named
"Lucas Interpretation". This has been implemented in a prototype, which has
been proved useful in educational practice and has gained academic relevance
with an emerging generation of educational mathematics assistants (EMA) based
on Computer Theorem Proving (CTP).
Automated Theorem Proving (ATP), i.e. deduction, is the most reliable
technology used to check user input. However ATP is inherently weak in
automatically generating solutions for arbitrary problems in applied
mathematics. This weakness is crucial for EMAs: when ATP checks user input as
incorrect and the learner gets stuck then the system should be able to suggest
possible next steps.
The key idea of Lucas Interpretation is to compute the steps of a calculation
following a program written in a novel CTP-based programming language, i.e.
computation provides the next steps. User guidance is generated by combining
deduction and computation: the latter is performed by a specific language
interpreter, which works like a debugger and hands over control to the learner
at breakpoints, i.e. tactics generating the steps of calculation. The
interpreter also builds up logical contexts providing ATP with the data
required for checking user input, thus combining computation and deduction.
The paper describes the concepts underlying Lucas Interpretation so that open
questions can adequately be addressed, and prerequisites for further work are
provided.Comment: In Proceedings THedu'11, arXiv:1202.453
Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking
Model-based mutation testing uses altered test models to derive test cases
that are able to reveal whether a modelled fault has been implemented. This
requires conformance checking between the original and the mutated model. This
paper presents an approach for symbolic conformance checking of action systems,
which are well-suited to specify reactive systems. We also consider
nondeterminism in our models. Hence, we do not check for equivalence, but for
refinement. We encode the transition relation as well as the conformance
relation as a constraint satisfaction problem and use a constraint solver in
our reachability and refinement checking algorithms. Explicit conformance
checking techniques often face state space explosion. First experimental
evaluations show that our approach has potential to outperform explicit
conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment
The area of geometry with its very strong and appealing visual contents and
its also strong and appealing connection between the visual content and its
formal specification, is an area where computational tools can enhance, in a
significant way, the learning environments.
The dynamic geometry software systems (DGSs) can be used to explore the
visual contents of geometry. This already mature tools allows an easy
construction of geometric figures build from free objects and elementary
constructions. The geometric automated theorem provers (GATPs) allows formal
deductive reasoning about geometric constructions, extending the reasoning via
concrete instances in a given model to formal deductive reasoning in a
geometric theory.
An adaptative and collaborative blended-learning environment where the DGS
and GATP features could be fully explored would be, in our opinion a very rich
and challenging learning environment for teachers and students.
In this text we will describe the Web Geometry Laboratory a Web environment
incorporating a DGS and a repository of geometric problems, that can be used in
a synchronous and asynchronous fashion and with some adaptative and
collaborative features.
As future work we want to enhance the adaptative and collaborative aspects of
the environment and also to incorporate a GATP, constructing a dynamic and
individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453
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