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Today, concurrent programming has become mainstream, dictated by need for ever increasing performance which, having reached the end of Moore’s law, can only be achieved by parallelism. Indeed, application software from areas such as medicine or natural sciences heavily relies on parallel hardware infrastructure like (GP)GPU accelerators, FPGAs, and multi- and many-core machines. However, it is also today that we see concurrency faults coming up every day. The simple reason is that writing concurrent programs is difficult. Most programmers “think sequentially” and therefore make mistakes when writing concurrent software. Notorious programming errors include deadlock and violations of atomicity or order of operations, which are mainly caused by the wrong use of synchronization primitives like semaphores or locks. Even worse, the inherent non-deterministic behavior of concurrent software makes bugs difficult to reproduce. Addressing these challenges requires efforts from multiple related disciplines, involving concurrency bug detection, program testing and validation, and programming language design. Another important area of computer science where concurrency naturally arises is that of reactive systems, which maintain an ongoing interaction with their environment. In contrast to sequential systems whose meaning is defined by the results of finite computations, the behavior of reactive systems is mainly determined by concurrent execution, communication, interaction, and mobility of non-terminating processes. Typical examples include operating systems, control systems for production lines, power plants, or vehicles. As many of such systems are safety critical, their development calls for rigorous formal techniques for design, implementation, and validation. The aim of this course is to provide a basic understanding of modeling formalisms for concurrent systems. It will address two basic approaches, which are respectively called the interleaving and the true concurrency approach. The former is based on the idea to reduce the phenomenon of concurrency to well-known concepts, by interpreting parallel behavior as non-deterministic merging of sequential execution. It is represented by various process algebras, which provide a formal apparatus for reasoning about structure and behaviour of systems in a compositional way. The true concurrency approach mainly comes in the form of Petri nets, which are well suited for explicitly modeling the concurrent behavior of distributed systems.

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今日、並行プログラミングは主流になっており、ムーアの法則の終わりに達したパフォーマンスの向上が必要であり、これは並列処理によってのみ達成できます。実際、医学や自然科学などの分野のアプリケーションソフトウェアは、（GP）GPUアクセラレータ、FPGA、

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Today, concurrent programming has become mainstream, requiring performance improvements that have reached the end of Moore's Law, which can only be achieved with parallel processing. In fact, application software in fields such as medicine and natural sciences (GP) GPU accelerators,

INTO JAPANESE

今日、並行プログラミングが主流になっており、ムーアの法則の終わりに達したパフォーマンスの改善が必要になりましたが、これは並列処理でのみ達成できます。実際、医学や自然科学（GP）GPUアクセラレータなどの分野のアプリケーションソフトウェアは、

BACK INTO ENGLISH

Today, concurrent programming has become mainstream, requiring performance improvements that have reached the end of Moore's Law, which can only be achieved with parallel processing. In fact, application software in fields such as medicine and natural science (GP) GPU accelerators

INTO JAPANESE

今日、並行プログラミングが主流になっており、ムーアの法則の終わりに達したパフォーマンスの改善が必要になりましたが、これは並列処理でのみ達成できます。実際、医学や自然科学（GP）GPUアクセラレータなどの分野のアプリケーションソフトウェア

BACK INTO ENGLISH

Today, concurrent programming has become mainstream, requiring performance improvements that have reached the end of Moore's Law, which can only be achieved with parallel processing. In fact, application software in fields such as medicine and natural science (GP) GPU accelerators