Invariants in Bounded Counter: Understanding Inductive Invariants

In course

Description

This lecture by the instructor delves into the concept of invariants in a bounded counter system, exploring properties satisfied by reachable states and the notion of inductive invariants. Through examples and exercises, the lecture demonstrates how inductive invariants strengthen the understanding of system behavior and help prove the correctness of properties. The lecture also covers the practical application of invariants in verifying system behaviors and the importance of algorithms like bounded model checking and model checking using binary decision diagrams.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_qn9a9xy4

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Related concepts (21)

In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language.

In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code.

Runtime verification is a computing system analysis and execution approach based on extracting information from a running system and using it to detect and possibly react to observed behaviors satisfying or violating certain properties. Some very particular properties, such as datarace and deadlock freedom, are typically desired to be satisfied by all systems and may be best implemented algorithmically. Other properties can be more conveniently captured as formal specifications.

This article describes Kripke structures as used in model checking. For a more general description, see Kripke semantics. A Kripke structure is a variation of the transition system, originally proposed by Saul Kripke, used in model checking to represent the behavior of a system. It consists of a graph whose nodes represent the reachable states of the system and whose edges represent state transitions, together with a labelling function which maps each node to a set of properties that hold in the corresponding state.

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