On the complexity of determinizing monitors

We examine the determinization of monitors. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor. When monitors are described as CCS-like processes, this doubly-exponential bound is optimal. When (deterministic) monitors are described as finite automata (as their LTS), then they can be exponentially more succinct than their CCS process form.peer-reviewe

The Cost of Monitoring Alone

We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential blowup in the syntactic size of the monitors, and a triple-exponential blowup when the goal is a deterministic monitor. We show that these bounds are tight and that they also hold for translations between corresponding fragments of Hennessy-Milner logic with recursion over infinite traces.Comment: 22 page

Monitoring for Silent Actions

Silent actions are an essential mechanism for system modelling and specification. They are used to abstractly report the occurrence of computation steps without divulging their precise details, thereby enabling the description of important aspects such as the branching structure of a system. Yet, their use rarely features in specification logics used in runtime verification. We study monitorability aspects of a branching-time logic that employs silent actions, identifying which formulas are monitorable for a number of instrumentation setups. We also consider defective instrumentation setups that imprecisely report silent events, and establish monitorability results for tolerating these imperfections

The Best a Monitor Can Do

Existing notions of monitorability for branching-time properties are fairly restrictive. This, in turn, impacts the ability to incorporate prior knowledge about the system under scrutiny - which corresponds to a branching-time property - into the runtime analysis. We propose a definition of optimal monitors that verify the best monitorable under- or over-approximation of a specification, regardless of its monitorability status. Optimal monitors can be obtained for arbitrary branching-time properties by synthesising a sound and complete monitor for their strongest monitorable consequence. We show that the strongest monitorable consequence of specifications expressed in Hennessy-Milner logic with recursion is itself expressible in this logic, and present a procedure to find it. Our procedure enables prior knowledge to be optimally incorporated into runtime monitors

Bidirectional Runtime Enforcement of First-Order Branching-Time Properties

Runtime enforcement is a dynamic analysis technique that instruments a monitor with a system in order to ensure its correctness as specified by some property. This paper explores bidirectional enforcement strategies for properties describing the input and output behaviour of a system. We develop an operational framework for bidirectional enforcement and use it to study the enforceability of the safety fragment of Hennessy-Milner logic with recursion (sHML). We provide an automated synthesis function that generates correct monitors from sHML formulas, and show that this logic is enforceable via a specific type of bidirectional enforcement monitors called action disabling monitors

Formal Approaches to Control System Security From Static Analysis to Runtime Enforcement

With the advent of Industry 4.0, industrial facilities and critical infrastructures are transforming into an ecosystem of heterogeneous physical and cyber components, such as programmable logic controllers, increasingly interconnected and therefore exposed to cyber-physical attacks, i.e., security breaches in cyberspace that may adversely affect the physical processes underlying industrial control systems. The main contributions of this thesis follow two research strands that address the security concerns of industrial control systems via formal methodologies. As our first contribution, we propose a formal approach based on model checking and statistical model checking, within the MODEST TOOLSET, to analyse the impact of attacks targeting nontrivial control systems equipped with an intrusion detection system (IDS) capable of detecting and mitigating attacks. Our goal is to evaluate the impact of cyber-physical attacks, i.e., attacks targeting sensors and/or actuators of the system with potential consequences on the safety of the inner physical process. Our security analysis estimates both the physical impact of the attacks and the performance of the IDS. As our second contribution, we propose a formal approach based on runtime enforcement to ensure specification compliance in networks of controllers, possibly compromised by colluding malware that may tamper with actuator commands, sensor readings, and inter-controller communications. Our approach relies on an ad-hoc sub-class of Ligatti et al.’s edit automata to enforce controllers represented in Hennessy and Regan’s Timed Process Language. We define a synthesis algorithm that, given an alphabet P of observable actions and a timed correctness property e, returns a monitor that enforces the property e during the execution of any (potentially corrupted) controller with alphabet P, and complying with the property e. Our monitors correct and suppress incorrect actions coming from corrupted controllers and emit actions in full autonomy when the controller under scrutiny is not able to do so in a correct manner. Besides classical requirements, such as transparency and soundness, the proposed enforcement enjoys deadlock- and diverge-freedom of monitored controllers, together with compositionality when dealing with networks of controllers. Finally, we test the proposed enforcement mechanism on a non-trivial case study, taken from the context of industrial water treatment systems, in which the controllers are injected with different malware with different malicious goals

Developing theoretical foundations for runtime enforcement

The ubiquitous reliance on software systems is increasing the need for ensuring their correctness. Runtime enforcement is a monitoring technique that uses moni- tors that can transform the actions of a system under scrutiny in order to alter its runtime behaviour and keep it in line with a correctness specification; these type of enforcement monitors are often called transducers. In runtime enforcement there is often no clear separation between the specification language describing the cor- rectness criteria that a system must satisfy, and the monitoring mechanism that actually ensures that these criteria are met. We thus aim to adopt a separation of concerns between the correctness specification describing what properties the sys- tem should satisfy, and the monitor describing how to enforce these properties. In this thesis we study the enforceability of the highly expressive branching time logic μHML, in a bid to identify a subset of this logic whose formulas can be adequately enforced by transducers at runtime. We conducted our study in relation to two different enforcement instrumentation settings, namely, a unidirectional setting that is simpler to understand and formalise but limited in the type of system actions it can transform at runtime, and a bidirectional one that, albeit being more complex, it allows transducers to effect and modify a wider set of system actions. During our investigation we define the behaviour of enforcement transducers and how they should be embedded with a system to achieve unidirectional and bidirectional enforcement. We also investigate what it means for a monitor to adequately enforce a logic formula, and define the necessary criteria that a monitor must satisfy in order to be adequate. Since enforcement monitors are highly intrusive, we also define a notion of optimality to use as a guide for identifying the least intrusive monitor that adequately enforces a formula. Using these enforcement definitions, we identify a μHML fragment that can be adequately enforced via enforcement transducers that drop the execution of certain actions. We then show that this fragment is maximally expressive, i.e., it is the largest subset that can be enforced via these type of enforcement monitors. We finally look into static alternatives to runtime enforcement and identify a static analysis technique that can also enforce the identified μHML fragment, but without requiring the system to execute