13 research outputs found
Domains for Higher-Order Games
We study two-player inclusion games played over word-generating higher-order
recursion schemes. While inclusion checks are known to capture verification
problems, two-player games generalize this relationship to program synthesis.
In such games, non-terminals of the grammar are controlled by opposing players.
The goal of the existential player is to avoid producing a word that lies
outside of a regular language of safe words.
We contribute a new domain that provides a representation of the winning
region of such games. Our domain is based on (functions over) potentially
infinite Boolean formulas with words as atomic propositions. We develop an
abstract interpretation framework that we instantiate to abstract this domain
into a domain where the propositions are replaced by states of a finite
automaton. This second domain is therefore finite and we obtain, via standard
fixed-point techniques, a direct algorithm for the analysis of two-player
inclusion games. We show, via a second instantiation of the framework, that our
finite domain can be optimized, leading to a (k+1)EXP algorithm for order-k
recursion schemes. We give a matching lower bound, showing that our approach is
optimal. Since our approach is based on standard Kleene iteration, existing
techniques and tools for fixed-point computations can be applied.Comment: Conference version accepted for presentation and publication at the
42nd International Symposium on Mathematical Foundations of Computer Science
(MFCS 2017
Computer Aided Verification
The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency
Computer Aided Verification
The open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency