There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The discovery that mammalian cells generate nitric oxide, a gas previously considered to be merely an atmospheric pollutant, is providing important information about many biologic processes. Nitric oxide is synthesized from the amino acid L-arginine by a family of enzymes, the nitric oxide synthases, through a hitherto unrecognized metabolic route -- namely, the L-arginine-nitric oxide pathway1–8. The synthesis of nitric oxide by vascular endothelium is responsible for the vasodilator tone that is essential for the regulation of blood pressure. In the central nervous system nitric oxide is a neurotransmitter that underpins several functions, including the formation of memory. . . .

The L-Arginine-Nitric Oxide Pathway

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Convex Analysisの二,三の進展について

Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

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Principles of Model Checking

ATS/ACCP statement on cardiopulmonary exercise testing.

Dominoes and the complexity of subclasses of logical theories

State Machines: Verification Problems and Complexity

Abstract state machines: verification problems and complexity

The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study Solitaire-LFP, a fragment of least fixed- point logic, whose evaluation games are nested soltaire games. This means that on each strongly connected component of the game, only one player can make nontrivial moves. Winning sets of nested solitaire games can be computed efficiently. The model-checking problem for Solitaire-LFP is PSPACE-complete in general and PTIME-complete for formulae of bounded width. On finite structures (but not on infinite ones), Solitaire-LFP is equivalent to transitive closure logic. We also consider the solitaire fragment of guarded fixed-point logics. Due to the restricted quantification pattern of these logics, the associated games are small and therefore admit more efficient model-checking algorithms.

Fixed-Point Logics and Solitaire Games

We study the logical definablity of the winning regions of parity games For games with a bounded number of priorities, it is well-known that the winning regions are definable in the modal μ-calculus Here we investigate the case of an unbounded number of priorities, both for finite game graphs and for arbitrary ones In the general case, winning regions are definable in guarded second-order logic (GSO), but not in least-fixed point logic (LFP) On finite game graphs, winning regions are LFP-definable if, and only if, they are computable in polynomial time, and this result extends to any class of finite games that is closed under taking bisimulation quotients

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Erich Grädel

Papers

Dominoes and the complexity of subclasses of logical theories

Abstract state machines: verification problems and complexity

Fixed-Point Logics and Solitaire Games

The Descriptive Complexity of Parity Games

Infinite graphs generated by tree rewriting