This study examines the use of counterexamples for supporting development students’ algorithmic thinking. Working from premise that some are more effective than others generalized algorithms, proposes distinctions between in relation to iterative refinement student-invented algorithms. Furthermore, identifies factors may influence differences among counterexamples. Using task-based interviews, ...

ion Refinement for Termination⋆ Byron Cook, Andreas Podelski, and Andrey Rybalchenko 1 Microsoft Research, Cambridge 2 Max-Planck-Institut für Informatik, Saarbrücken Abstract. Abstraction can often lead to spurious counterexamples. Counterexample-guided abstraction refinement is a method of strengthening abstractions based on the analysis of these spurious counterexamples. For invariance prope...

Counterexamples explain why a desired temporal logic property fails to hold. The generation of counterexamples is considered to be one of the primary advantages of model checking as a verification technique. Furthermore, when model checking does succeed in verifying a property, there is typically no independently checkable witness that can be used as evidence for the verified property. Previous...

Since counterexamples generated by model checking tools are only symptoms of faults in the model, a significant amount of manual work is required in order to locate the fault that is the root cause for the presence of counterexamples in the model. In this paper, we propose an automated method for explaining counterexamples that are symptoms of the occurrence of deadlocks in concurrent systems. ...

Say that f : {0, 1}n → {0, 1} 2-approximates g : {0, 1}n → {0, 1} if the functions disagree on at most an 2 fraction of points. This paper contains two results about approximation by DNF and other small-depth circuits: (1) For every constant 0 < 2 < 1/2 there is a DNF of size 2 √ n) that 2-approximates the Majority function on n bits, and this is optimal up to the constant in the exponent. (2) ...

Andrew Baker’s approach to reasoning about actions is the most robust circumscriptive approach currently known. Investigation of its applicability to nondeterministic actions reveals that this approach does not allow us to draw some intuitively plausible conclusions. Also, it does not always generate the proper existence of situations axiom. The limitations are traced to an unexpected interfere...

The classical Tarski theorem on topological semantics of modal logic states that the logic S4 is complete in R for each n. Recently several authors have considered logics of dynamic topological systems, which is a topological space and a function on it. In [1] a bimodal logic S4C was introduced and proven to be complete with respect to the class of all continuous dynamic systems. A number of po...

Lauritz Munch and Björn Lundgren have recently replied to a paper published by us in this journal. In our original paper, we defended novel version of the so-called ‘control theory’ moral right privacy. We argued that control theorists should define ‘control’ as what coined ‘Negative Control’. provided range interesting challenging objections view. Independently each other, they give almost ide...