10,385 research outputs found
The Structure of Differential Invariants and Differential Cut Elimination
The biggest challenge in hybrid systems verification is the handling of
differential equations. Because computable closed-form solutions only exist for
very simple differential equations, proof certificates have been proposed for
more scalable verification. Search procedures for these proof certificates are
still rather ad-hoc, though, because the problem structure is only understood
poorly. We investigate differential invariants, which define an induction
principle for differential equations and which can be checked for invariance
along a differential equation just by using their differential structure,
without having to solve them. We study the structural properties of
differential invariants. To analyze trade-offs for proof search complexity, we
identify more than a dozen relations between several classes of differential
invariants and compare their deductive power. As our main results, we analyze
the deductive power of differential cuts and the deductive power of
differential invariants with auxiliary differential variables. We refute the
differential cut elimination hypothesis and show that, unlike standard cuts,
differential cuts are fundamental proof principles that strictly increase the
deductive power. We also prove that the deductive power increases further when
adding auxiliary differential variables to the dynamics
Quantifier-Free Interpolation of a Theory of Arrays
The use of interpolants in model checking is becoming an enabling technology
to allow fast and robust verification of hardware and software. The application
of encodings based on the theory of arrays, however, is limited by the
impossibility of deriving quantifier- free interpolants in general. In this
paper, we show that it is possible to obtain quantifier-free interpolants for a
Skolemized version of the extensional theory of arrays. We prove this in two
ways: (1) non-constructively, by using the model theoretic notion of
amalgamation, which is known to be equivalent to admit quantifier-free
interpolation for universal theories; and (2) constructively, by designing an
interpolating procedure, based on solving equations between array updates.
(Interestingly, rewriting techniques are used in the key steps of the solver
and its proof of correctness.) To the best of our knowledge, this is the first
successful attempt of computing quantifier- free interpolants for a variant of
the theory of arrays with extensionality
Semantics-based Automated Web Testing
We present TAO, a software testing tool performing automated test and oracle
generation based on a semantic approach. TAO entangles grammar-based test
generation with automated semantics evaluation using a denotational semantics
framework. We show how TAO can be incorporated with the Selenium automation
tool for automated web testing, and how TAO can be further extended to support
automated delta debugging, where a failing web test script can be
systematically reduced based on grammar-directed strategies. A real-life
parking website is adopted throughout the paper to demonstrate the effectivity
of our semantics-based web testing approach.Comment: In Proceedings WWV 2015, arXiv:1508.0338
On Algorithms and Complexity for Sets with Cardinality Constraints
Typestate systems ensure many desirable properties of imperative programs,
including initialization of object fields and correct use of stateful library
interfaces. Abstract sets with cardinality constraints naturally generalize
typestate properties: relationships between the typestates of objects can be
expressed as subset and disjointness relations on sets, and elements of sets
can be represented as sets of cardinality one. Motivated by these applications,
this paper presents new algorithms and new complexity results for constraints
on sets and their cardinalities. We study several classes of constraints and
demonstrate a trade-off between their expressive power and their complexity.
Our first result concerns a quantifier-free fragment of Boolean Algebra with
Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for
reducing the satisfiability of sets with symbolic cardinalities to constraints
on constant cardinalities, and give a polynomial-space algorithm for the
resulting problem.
In a quest for more efficient fragments, we identify several subclasses of
sets with cardinality constraints whose satisfiability is NP-hard. Finally, we
identify a class of constraints that has polynomial-time satisfiability and
entailment problems and can serve as a foundation for efficient program
analysis.Comment: 20 pages. 12 figure
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