Stefan Andrei

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Testing constraints for real-time systems are usually verified through the satisfiability of propositional formulae. In this paper, we propose an alternative where the verification of timing constraints can be done by counting the number of truth assignments instead of Boolean satisfiability. This number can also tell us how "far away" a given specification(More)
This paper refers to the Collatz conjecture. The origin and the formalization of the Collatz problem are presented in the first section, named “Introduction”. In the second section, entitled “Properties of the Collatz function”, we treat mainly the bijectivity of the Collatz function. Using the obtained results, we construct a (set of) binary tree(s) which(More)
Given a task set T, determining the number of processors leading to a feasible schedule for T is an important problem in the real-time embedded systems community. For periodic and independent task sets, the utilization rate represents a lower bound on the number of processors. A multiprocessor platform with fewer processors than the utilization rate of a(More)
Affine size-change analysis has been used for termination analysis of eager functional programming languages. The same style of analysis is also capable of compactly recording and calculating other properties of programs, including their runtime, maximum stack depth, and (relative) path time costs. In this paper we show how precise (not just big-O)(More)
Constructive methods for obtaining regular grammar counterparts for some sub-classes of context-free grammars (CFGs) have been investigated by many researchers. An important class of grammars for which this is always possible is the one-letter CFG. We show in this paper a new constructive method for transforming an arbitrary one-letter CFG to an equivalent(More)
The paper refers to the Collatz's conjecture. In the first part, we present some equivalent forms of this conjecture and a slight generalization of a former result from [1]. Then, we present the notion of “chain subtrees” in Collatz's tree followed by a characterization theorem and some subclass of numbers which are labels for some chain subtrees. Next, we(More)
Real-time logic (RTL) is useful for the verification of a safety assertion SA with respect to the specification SP of a real-time system. Since the satisfiability problem for RTL is undecidable, there were many efforts to find proper heuristics for proving that SPrarrSA holds. However, none of such heuristics necessarily finds an "optimal implication".(More)
We present a new algorithm for counting truth assignments of a clausal formula using inverse propositional resolution and its associated normalization rules. The idea is opposite of the classical resolution, and is achieved by constructing in a bottom-up manner a computation graph. This means that we successively add complementary literals to generate new(More)