A parameterized halting problem, the linear time hierarchy, and the MRDP theorem

The complexity of the parameterized halting problem for nondeterministic Turing machines p-Halt is known to be related to the question of whether there are logics capturing various complexity classes [10]. Among others, if p-Halt is in para-AC0, the parameterized version of the circuit complexity class AC0, then AC0, or equivalently, (+, x)-invariant FO, has a logic. Although it is widely believed that p-Halt ∉. para-AC0, we show that the problem is hard to settle by establishing a connection to the question in classical complexity of whether NE ⊈ LINH. Here, LINH denotes the linear time hierarchy. On the other hand, we suggest an approach toward proving NE ⊈ LINH using bounded arithmetic. More specifically, we demonstrate that if the much celebrated MRDP (for Matiyasevich-Robinson-Davis-Putnam) theorem can be proved in a certain fragment of arithmetic, then NE ⊈ LINH. Interestingly, central to this result is a para-AC0 lower bound for the parameterized model-checking problem for FO on arithmetical structures.Peer ReviewedPostprint (author's final draft

Optimal algorithms and proofs (Dagstuhl Seminar 14421)

This report documents the programme and the outcomes of the Dagstuhl Seminar 14421 "Optimal algorithms and proofs". The seminar brought together researchers working in computational and proof complexity, logic, and the theory of approximations. Each of these areas has its own, but connected notion of optimality; and the main aim of the seminar was to bring together researchers from these different areas, for an exchange of ideas, techniques, and open questions, thereby triggering new research collaborations across established research boundaries

Model Transformation Languages with Modular Information Hiding

Model transformations, together with models, form the principal artifacts in model-driven software development. Industrial practitioners report that transformations on larger models quickly get sufficiently large and complex themselves. To alleviate entailed maintenance efforts, this thesis presents a modularity concept with explicit interfaces, complemented by software visualization and clustering techniques. All three approaches are tailored to the specific needs of the transformation domain

Model Transformation Languages with Modular Information Hiding

Model transformations, together with models, form the principal artifacts in model-driven software development. Industrial practitioners report that transformations on larger models quickly get sufficiently large and complex themselves. To alleviate entailed maintenance efforts, this thesis presents a modularity concept with explicit interfaces, complemented by software visualization and clustering techniques. All three approaches are tailored to the specific needs of the transformation domain

Programs as Diagrams: From Categorical Computability to Computable Categories

This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later chapters contain new ideas and results about categorical computability and some first steps into computable category theory. The underlying categorical view of computation is based on monoidal categories with program evaluators, called *monoidal computers*. This categorical structure can be viewed as a single-instruction diagrammatic programming language called Run, whose only instruction is called RUN. This version: improved text, moved the final chapter to the next volume. (The final version will continue lots of exercises and workouts, but already this version has severely degraded graphics to meet the size bounds.)Comment: 150 pages, 81 figure

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Automatic synthesis of component & connector software architectures with bounded combinatory logic

Combinatory logic synthesis is a new type-based approach towards automatic synthesis of software from components in a repository. In this thesis we show how the type-based approach can naturally be used to exploit taxonomic conceptual structures in software architectures and component repositories to enable automatic composition and configuration of components, and also code generation, by associating taxonomic concepts to architectural building blocks such as, in particular, software connectors. Components of a repository are exposed for synthesis as typed combinators, where intersection types are used to represent concepts that specify intended usage and functionality of a component. An algorithm for solving the type inhabitation problem in combinatory logic - does there exist a composition of combinators with a given type? - is then used to automate the retrieval, composition, and configuration of suitable building blocks with respect to a goal specification. Since type inhabitation has high computational complexity, heuristic optimizations for the inhabitation algorithm are essential for making the approach practical. We discuss particularly important (theoretical and pragmatic) optimization strategies and evaluate them by experiments. Furthermore, we apply this synthesis approach to define a method for software connector synthesis for realistic software architectures based on a type theoretic model. We conduct experiments with a rapid prototyping tool that employs this method on complex concrete ERP- and e-Commerce-systems and discuss the results