4,268 research outputs found
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
Towards the Formalization of Fractional Calculus in Higher-Order Logic
Fractional calculus is a generalization of classical theories of integration
and differentiation to arbitrary order (i.e., real or complex numbers). In the
last two decades, this new mathematical modeling approach has been widely used
to analyze a wide class of physical systems in various fields of science and
engineering. In this paper, we describe an ongoing project which aims at
formalizing the basic theories of fractional calculus in the HOL Light theorem
prover. Mainly, we present the motivation and application of such formalization
efforts, a roadmap to achieve our goals, current status of the project and
future milestones.Comment: 9 page
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