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COMPLEXITY HIERARCHIES BEYOND ELEMENTARY
"... Abstract. We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinato ..."
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Abstract. We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond. 1.
The Power of Priority Channel Systems ∗
, 1301
"... We introduce Priority Channel Systems, a new class of channel systems where messages carry a numeric priority and where higherpriority messages can supersede lowerpriority messages preceding them in the fifo communication buffers. The decidability of safety and inevitability properties is shown vi ..."
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We introduce Priority Channel Systems, a new class of channel systems where messages carry a numeric priority and where higherpriority messages can supersede lowerpriority messages preceding them in the fifo communication buffers. The decidability of safety and inevitability properties is shown via the introduction of a priority embedding, a wellquasiordering that has not previously been used in wellstructured systems. We then show how Priority Channel Systems can compute FastGrowing functions and prove that the aforementioned verification problems are Fε0complete. 1
Keeping a crowd safe: On the complexity of parameterized verification (invited talk
 STACS, volume 25 of LIPIcs
, 2014
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Handling infinitely branching WSTS
 In Proceedings of ICALP’14 – Part II, LNCS
, 2014
"... Abstract. Most decidability results concerning wellstructured transition systems apply to the finitely branching variant. Yet some models (inserting automata, ωPetri nets,...) are naturally infinitely branching. Here we develop tools to handle infinitely branching WSTS by exploiting the crucial p ..."
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Abstract. Most decidability results concerning wellstructured transition systems apply to the finitely branching variant. Yet some models (inserting automata, ωPetri nets,...) are naturally infinitely branching. Here we develop tools to handle infinitely branching WSTS by exploiting the crucial property that in the (ideal) completion of a wellquasiordered set, downwardclosed sets are finite unions of ideals. Then, using these tools, we derive decidability results and we delineate the undecidability frontier in the case of the termination, the controlstate maintainability and the coverability problems. Coverability and boundedness under new effectivity conditions are shown decidable. 1
COMPLEXITY BOUNDS FOR ORDINALBASED TERMINATION
"... Abstract. ‘What more than its truth do we know if we have a proof of a theorem in a given formal system? ’ We examine Kreisel’s question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length func ..."
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Abstract. ‘What more than its truth do we know if we have a proof of a theorem in a given formal system? ’ We examine Kreisel’s question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.