Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userReLIC: Reduced Logic Inference for Composition for Quantifier Elimination based Compositional Reasoning and Verification
128
0
0.0
(
0
)
Added by
Hao Ren Ph.D.
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The paper presents our research on quantifier elimination (QE) for compositional reasoning and verification. For compositional reasoning, QE provides the foundation of our approach, serving as the calculus for composition to derive the strongest system-property in a single step, from the given component atomic-properties and their interconnection relation. We first developed this framework for time-independent properties, and later extended it to time-dependent property composition. The extension requires, in addition, shifting the given properties along time to span the time horizon of interest, he least of which for the strongest system-property is no more than the total time horizons of the component level atomic-properties. The system-initial-condition is also composed from atomic-initial-conditions of the components the same way. It is used to verify a desired system-level property, alongside the derived strongest system-property, by way of induction. Our composition approach is uniform regardless of the composition types (cascade/parallel/feedback) for both time-dependent and time-independent properties. We developed a new prototype verifier named ReLIC (Reduced Logic Inference for Composition) that implements our above approaches. We demonstrated it through several illustrative and practical examples. Further, we advanced the $k$-induction based model-checking with QE capabilities, by formulating its base and inductive steps into QE problems where all the variables are universally quantified. Our integration of the QE solver Redlog with the $k$-induction based model-checking tool JKind, shows the successful solving of a non-linear problem that the SMT capable JKind failed to resolve. Finally, we also showcase the recent adoption of our approaches within an industrial V&V tool suite for augmented static analysis of Simulink models and Deep Neural Networks (DNNs).
rate research
Read More
The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e. obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice.
We define a pi-calculus variant with a costed semantics where channels are treated as resources that must explicitly be allocated before they are used and can be deallocated when no longer required. We use a substructural type system tracking permission transfer to construct coinductive proof techniques for comparing behaviour and resource usage efficiency of concurrent processes. We establish full abstraction results between our coinductive definitions and a contextual behavioural preorder describing a notion of process efficiency w.r.t. its management of resources. We also justify these definitions and respective proof techniques through numerous examples and a case study comparing two concurrent implementations of an extensible buffer.
We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints induced by the synchronisations between components. The method has been implemented in the RTD-Finder tool and successfully experimented on several benchmarks.
Model checking probabilistic CTL properties of Markov decision processes with convex uncertainties has been recently investigated by Puggelli et al. Such model checking algorithms typically suffer from the state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDP while preserving the probabilistic CTL properties it satisfies. In particular, we discuss the key ingredients to build up the operations of parallel composition for composing interval MDP components at run-time. More precisely, we investigate how the parallel composition operator for interval MDPs can be defined so as to arrive at a congruence closure. As a result, we show that probabilistic bisimulation for interval MDPs is congruence with respect to two facets of parallelism, namely synchronous product and interleaving.
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the category of a monad of sets to the category of Boolean algebras, together with a uniquely determined system of quantifiers. A striking feature of this approach is that Cayleys Completeness Theorem and Godels Completeness Theorem can be stated and proved in a much simpler fashion for quantifier theories. Both theorems are due to Halmos for polyadic algebras. We also present a simple transparent treatment of ultraproducts of models of a quantifier theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
