Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Runtime verification on data-carrying traces

Malfunctioning software systems can cause severe loss of money, sensitive data, or even human life. The ambition is therefore to verify these systems not only statically, but also monitor their behaviour at runtime. For the latter case, the temporal logic LTL---a de facto standard specification formalism in runtime verification---is widely used and well-understood. However, propositional variables are usually not a natural nor sufficient model to represent the behaviour of complex, interactive systems that can process arbitrary input values. Consequently, there is a demand for more expressive formalisms that are defined what we call traces with data, i.e., traces that contain propositions enriched with values from a (possibly) infinite domain. This thesis studies the runtime monitoring with data for a natural extension of LTL that includes first-order quantification, called LTLFO. The logic's quantifiers range over values that appear in a trace. Under assumptions laid out of what should arguably be considered a ``proper'' runtime monitor, this thesis first identifies and analyses the underlying decision problems of monitoring properties in LTL and LTLFO. Moreover, it proposes a monitoring procedure for the latter. A result is that LTLFO is undecidable, and the prefix problem too, which an online monitor has to preferably solve to coincide with monotonicity. Hence, the obtained monitor cannot be complete for LTLFO; however, this thesis proves the soundness of its construction and gives experimental results from an implementation, in order to justify its usefulness and efficiency in practice. The monitor is based on a new type of automaton, called spawning automaton; it helps to efficiently decide what parts of a possibly infinite state space need to be memorised at runtime. Furthermore, the problem occurs that not every property can be monitored trace-length independently, which is possible in LTL. For that reason, a hierarchy of effectively monitorable properties is proposed. It distinguishes properties for which a monitor requires only constant memory from ones for which a monitor inevitably has to grow ad infinitum, independently of how the future of a trace evolves. Last but not least, a proof of concept validates the monitoring means developed in this thesis on a widely established system with intensive data use: Malicious behaviour is checked on Android devices based on the most comprehensive malware set presently available. The overall detection and false positive rates are 93.9% and 28%, respectively. As a means of conducting the experiments and as a contribution in itself, an application-agnostic logging-layer for the Android system has been developed and its technical insights are explained. It aims at leveraging runtime verification techniques on Android, like other domain-specific instrumentation approaches did, such as AspectJ for Java

Reasoning short cuts in infinite domain constraint satisfaction: Algorithms and lower bounds for backdoors

A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere, and the algorithmic problem of finding such backdoors has consequently been intensively studied. Sioutis and Janhunen (KI, 2019) have proposed a generalised backdoor concept suitable for infinite-domain CSP instances over binary constraints. We generalise their concept into a large class of CSPs that allow for higher-arity constraints. We show that this kind of infinite-domain backdoors have many of the positive computational properties that finite-domain backdoors have: the associated computational problems are fixed-parameter tractable whenever the underlying constraint language is finite. On the other hand, we show that infinite languages make the problems considerably harder