Viability games on valence systems over graph monoids admit a complete decidability and complexity classification, with decidable cases in pushdown-counter combinations where non-termination games remain undecidable.
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A complete decidable characterization of polynomial rules P yielding bilinear associative commutative P-products on series is given, together with decidability of equivalence for the associated P-automata.
SPARQL, multiset Datalog, and multiset relational algebra are expressively equivalent for AND, UNION, FILTER, EXCEPT, and SELECT.
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Infinite-state Games with Energy Objectives Beyond Counters
Viability games on valence systems over graph monoids admit a complete decidability and complexity classification, with decidable cases in pushdown-counter combinations where non-termination games remain undecidable.
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Commutative algebras of series
A complete decidable characterization of polynomial rules P yielding bilinear associative commutative P-products on series is given, together with decidability of equivalence for the associated P-automata.
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Multiset semantics in SPARQL, Relational Algebra and Datalog
SPARQL, multiset Datalog, and multiset relational algebra are expressively equivalent for AND, UNION, FILTER, EXCEPT, and SELECT.