Stefan Andrei

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Embedded and real-time systems are increasingly common and complex, requiring formal specification and verification in order to guarantee their satisfaction of desirable safety and timing requirements. Real-Time Logic (RTL) has been used to capture both the specification of a real-time system and the desirable safety assertions with respect to this system(More)
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)
In general, it is undecidable if an arbitrary context-free grammar has a regular solution. Past work has focused on special cases, such as one-letter grammars, non self-embedded grammars and the finite-language grammars, for which regular counterparts have been proven to exist. However, little is known about grammars with the self-embedded property. Using(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)
Both specification and verification of business processes are gaining more and more attention in the field. Most of the existing works in the last years are dealing with important, yet very specialized, issues. Among these, we can enumerate compensation constructs to cope with exceptions generated by long running business transactions, fully programmable(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)
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) (F. Jahanian et al., 1986, 1987, F. Wang et al., 1994) is useful for the verification of a safety assertion with respect to the specification of a real-time system. Since the satisfiability problem for RTL is undecidable, the systematic debugging of a real-time system appears impossible. This paper provides a first step towards this(More)