The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

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Languages, automata, and logic

Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear-time model-checking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automata-theoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for model-checking. Recently, Bernholtz and Grumberg [1993] have shown that this exponential penalty can be avoided, though they did not match the linear complexity of non-automata-theoretic algorithms. In this paper, we show that alternating tree automata are the key to a comprehensive automata-theoretic framework for branching temporal logics. Not only can they be used to obtain optimal decision procedures, as was shown by Muller et al., but, as we show here, they also make it possible to derive optimal model-checking algorithms. Moreover, the simple combinatorial structure that emerges from the automata-theoretic approach opens up new possibilities for the implementation of branching-time model checking and has enabled us to derive improved space complexity bounds for this long-standing problem.

An automata-theoretic approach to branching-time model checking

Infinite games on finitely coloured graphs with applications to automata on infinite trees

Thiopurine methyltransferase (TPMT) activity exhibits monogenic co-dominant inheritance, with ethnic differences in the frequency of occurrence of variant alleles. With conventional thiopurine doses, homozygous TPMT-deficient patients (~1 in 178 to 1 in 3,736 individuals with two nonfunctional TPMT alleles) experience severe myelosuppression, 30-60% of individuals who are heterozygotes (~3-14% of the population) show moderate toxicity, and homozygous wild-type individuals (~86-97% of the population) show lower active thioguanine nucleolides and less myelosuppression. We provide dosing recommendations (updates at http://www.pharmgkb.org) for azathioprine, mercaptopurine (MP), and thioguanine based on TPMT genotype.

https://ascpt.onlinelibrary.wiley.com/doi/epdf/10.1038/clpt.2010.320

Clinical Pharmacogenetics Implementation Consortium guidelines for thiopurine methyltransferase genotype and thiopurine dosing.

This paper presents algorithms for the automatic synthesis of real-time controllers by finding a winning strategy for certain games defined by the timed-automata of Alur and Dill. In such games, the outcome depends on the players' actions as well as on their timing. We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications.

On the synthesis of discrete controllers for timed systems

It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the mu-calculus, the equivalence provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results. It is also shown how mu-calculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms. >

C.S. Jutla

Papers

Tree automata, mu-calculus and determinacy