A theory of register monitors ACM/IEEE Symposium on Logic in Computer Science Ferrere, Thomas ; https://orcid.org/0000-0001-5199-3143 Henzinger, Thomas A ; https://orcid.org/0000−0002−2985−7724 Saraç, Ege 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. IEEE 2018 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/144 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1145/3209108.3209194 info:eu-repo/semantics/altIdentifier/wos/000545262800041 info:eu-repo/semantics/closedAccess