conference paper published yes Thomas Ferrere author 40960E6E-F248-11E8-B48F-1D18A9856A870000-0001-5199-3143 Thomas A Henzinger author 40876CD8-F248-11E8-B48F-1D18A9856A870000−0002−2985−7724 Ege Saraç author ToHe department LICS: Logic in Computer Science The task of a monitor is to watch, at run-time, the execution of a reactive system, and signal the occurrence of a safety violation in the observed sequence of events. While finite-state monitors have been studied extensively, in practice, monitoring software also makes use of unbounded memory. We define a model of automata equipped with integer-valued registers which can execute only a bounded number of instructions between consecutive events, and thus can form the theoretical basis for the study of infinite-state monitors. We classify these register monitors according to the number k of available registers, and the type of register instructions. In stark contrast to the theory of computability for register machines, we prove that for every k 1, monitors with k + 1 counters (with instruction set 〈+1, =〉) are strictly more expressive than monitors with k counters. We also show that adder monitors (with instruction set 〈1, +, =〉) are strictly more expressive than counter monitors, but are complete for monitoring all computable safety -languages for k = 6. Real-time monitors are further required to signal the occurrence of a safety violation as soon as it occurs. The expressiveness hierarchy for counter monitors carries over to real-time monitors. We then show that 2 adders cannot simulate 3 counters in real-time. Finally, we show that real-time adder monitors with inequalities are as expressive as real-time Turing machines. IEEE2018Oxford, UK eng 00054526280004110.1145/3209108.3209194 Part F138033394 - 403 Ferrere, T., Henzinger, T. A., &#38; Saraç, E. (2018). A theory of register monitors (Vol. Part F138033, pp. 394–403). Presented at the LICS: Logic in Computer Science, Oxford, UK: IEEE. <a href="https://doi.org/10.1145/3209108.3209194">https://doi.org/10.1145/3209108.3209194</a> T. Ferrere, T.A. Henzinger, E. Saraç, in:, IEEE, 2018, pp. 394–403. Ferrere T, Henzinger TA, Saraç E. 2018. A theory of register monitors. LICS: Logic in Computer Science, ACM/IEEE Symposium on Logic in Computer Science, vol. Part F138033, 394–403. Ferrere, Thomas, Thomas A Henzinger, and Ege Saraç. “A Theory of Register Monitors,” Part F138033:394–403. IEEE, 2018. <a href="https://doi.org/10.1145/3209108.3209194">https://doi.org/10.1145/3209108.3209194</a>. T. Ferrere, T. A. Henzinger, and E. Saraç, “A theory of register monitors,” presented at the LICS: Logic in Computer Science, Oxford, UK, 2018, vol. Part F138033, pp. 394–403. Ferrere T, Henzinger TA, Saraç E. A theory of register monitors. In: Vol Part F138033. IEEE; 2018:394-403. doi:<a href="https://doi.org/10.1145/3209108.3209194">10.1145/3209108.3209194</a> Ferrere, Thomas, et al. <i>A Theory of Register Monitors</i>. Vol. Part F138033, IEEE, 2018, pp. 394–403, doi:<a href="https://doi.org/10.1145/3209108.3209194">10.1145/3209108.3209194</a>. 1442018-12-11T11:44:52Z2023-09-08T11:49:13Z