Related papers: Subcubic Certificates for CFL Reachability
Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
In this paper we study the fine-grained complexity of the CFL reachability problem. We first present one of the existing algorithms for the problem and an overview of conditional lower bounds based on widely believed hypotheses. We then use…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Context-free language (CFL) reachability is a standard approach in static analyses, where the analysis question is phrased as a language reachability problem on a graph $G$ wrt a CFL L. While CFLs lack the expressiveness needed for high…
Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
Certifying verification algorithms not only return whether a given property holds or not, but also provide an accompanying independently checkable certificate and a corresponding witness. The certificate can be used to easily validate the…
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified…
We revisit facial reduction from the point of view of projective geometry. This leads us to a homogenization strategy in conic programming that eliminates the phenomenon of weak infeasibility. For semidefinite programs (and others), this…
In the context of fine-grained complexity, we investigate the notion of certificate enabling faster polynomial-time algorithms. We specifically target radius (minimum eccentricity), diameter (maximum eccentricity), and all-eccentricity…
We present a fully automatic algorithm for verifying safety properties of parameterized software systems. This algorithm is based on both IC3 and Lazy Annotation. We implemented it in Cubicle, a model checker for verifying safety properties…
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have…
In PLDI'20, Lee et al. introduced the \emph{promising } semantics PS 2.0 of the C++ concurrency that captures most of the common program transformations while satisfying the DRF guarantee. The reachability problem for finite-state programs…
We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier…
Various static analysis problems are reformulated as instances of the Context-Free Language Reachability (CFL-r) problem. One promising way to make solving CFL-r more practical for large-scale interprocedural graphs is to reduce CFL-r to…