
On the size of disjunctive formulas in the ฮผcalculus
A key result in the theory of the modal mucalculus is the disjunctive n...
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One Theorem to Rule Them All: A Unified Translation of LTL into ฯAutomata
We present a unified translation of LTL formulas into deterministic Rabi...
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Combining Weak Distributive Laws: Application to UpTo Techniques
The coalgebraic modelling of alternating automata and of probabilistic a...
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A translation of weighted LTL formulas to weighted Bรผchi automata over ฯvaluation monoids
In this paper we introduce a weighted LTL over product ฯvaluation monoi...
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Revisiting MITL to Fix Decision Procedures
Metric Interval Temporal Logic (MITL) is a well studied realtime, tempo...
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Predicative proof theory of PDL and basic applications
Propositional dynamic logic (PDL) is presented in Schรผttestyle mode as ...
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An Optimal Construction for the BarthelmannSchwentick Normal Form on Classes of Structures of Bounded Degree
Building on the locality conditions for firstorder logic by Hanf and Ga...
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An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata
In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form โ_i=1^n ๐๐ ฯ_i โจ๐ ๐ฯ_i, where ฯ_i and ฯ_i contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalisation procedures have a nonelementary worstcase blowup, and follow an involved path from formulas to counterfree automata to starfree regular expressions and back to formulas. We improve on both points. We present a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blowup. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalises the formula, translates it into a special very weak alternating automaton, and applies a simple determinisation procedure, valid only for these special automata.
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