Inductive Reachability Witnesses

Ali Asadi; Krishnendu Chatterjee; Hongfei Fu; Amir Kafshdar Goharshady; Mohammad Mahdavi

Home/Archive/arXiv

arXiv · 2007.14259

Inductive Reachability Witnesses

Ali Asadi·Krishnendu Chatterjee·Hongfei Fu·Amir Kafshdar Goharshady·Mohammad Mahdavi

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works that tackle reachability analysis are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic/reverse Hoare logic). In contrast, we propose a novel approach for reachability analysis that can handle general programs, is (semi-)complete, and can be entirely automated for a wide family of programs. Our approach extends techniques from both invariant generation and ranking-function synthesis to reachability analysis through the notion of (Universal) Inductive Reachability Witnesses (IRWs/UIRWs). While traditional invariant generation uses over-approximations of reachable states, we consider the natural dual problem of under-approximating the set of program states that can reach a target state. We then apply an argument similar to ranking functions to ensure that all states in our under-approximation can indeed reach the target set in finitely many steps.

Explore related subjects

cs.PL cs.LO cs.SE

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ali Asadi, Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, Mohammad Mahdavi. 2020-07-28. Inductive Reachability Witnesses. https://arxiv.org/abs/2007.14259

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Expressive power of one-shot control operators and coroutines

Control operators, such as exceptions and effect handlers, provide a means of representing computational effects in programs abstractly and modularly. While most theoretical studies have focused on multi-shot control operators, one-shot control operators---which restrict the use of captured continuations to at most once---are gaining attention for their balance between expressiveness and efficiency. This study aims to fill the gap. We present a mathematically rigorous comparison of the expressive power among one-shot control operators, including effect handlers, delimited continuations, and even asymmetric coroutines. Following previous studies on multi-shot control operators, we adopt Felleisen's macro-expressiveness as our measure of expressiveness. We verify the folklore that one-shot effect handlers and one-shot delimited-control operators can be macro-expressed by asymmetric coroutines, but not vice versa. We explain why a previous informal argument fails, and how to revise it to make a valid macro-translation.

cs.PL↗

arXiv2026

Authorization Revocation for Long-Running AI Agents: Root-Scoped Quiescence under Delegation and Asynchronous Execution

Long-running AI agents outlive initiating processes through credentials, delegated tasks, queues, callbacks, reservations, and provider-side operations. Cancellation, process exit, and credential revocation neither close every pre-cut carrier nor distinguish independently authorized shared work. We define root-scoped authorization quiescence: for each manifested sink, a certificate accounts for every cut-relevant acceptance under the retired root-epoch atom that precedes its local fence and excludes protected acceptance under that atom after the fence, while permitting exact rebind to a current, independently sufficient support. The root-scoped quiescence protocol linearizes a root cut, fences old-root expansion and protected sinks, represents alternative and conjunctive authority as antichains of minimal sufficient root sets, and composes provider-frontier certificates into a cutset over registered old-root paths. Exact channel-token accounting reconciles transfers; missing or conflicting evidence remains indeterminate. Under stated assumptions, we prove post-cut issuer non-expansion, support-sound projection, compositional soundness under exact channel conservation, independent-support preservation, merge-order independence, and crash/replay stability. A provider-free late-effect test suite matches 17/17 registered outcomes. Two cancellation-only and one cut-only execution accept the same class of already scheduled late effect; two cut-plus-fence executions, one restart, and one stale-process execution reject it. A separately implemented checker verifies 17/17 traces and rejects 44/44 consistently rehashed semantic regressions. The certificate establishes root-relative authorization quiescence within its bound manifest and configuration, not global idleness, rollback, or business completion.

cs.PL↗

arXiv2026

Soda: An Object-Oriented Functional Language for Specifying Human-Centered Problems

We present Soda (Symbolic Objective Descriptive Analysis), a language that helps to treat qualities and quantities in a natural way and greatly simplifies the task of checking correctness. We present key properties for the language motivated by the design of a descriptive language to encode complex requirements on computer systems, and we explain how these key properties must be addressed to model these requirements with simple definitions. We give an overview of a tool that helps to describe problems in an easy way, which we consider more transparent and less error-prone.

cs.PL↗