Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Analysis of Generative Chemistries

For the modelling of chemistry we use undirected, labelled graphs as explicit models of molecules and graph transformation rules for modelling generalised chemical reactions. This is used to define artificial chemistries on the level of individual bonds and atoms, where formal graph grammars implicitly represent large spaces of chemical compounds. We use a graph rewriting formalism, rooted in category theory, called the Double Pushout approach, which directly expresses the transition state of chemical reactions. Using concurrency theory for transformation rules, we define algorithms for the composition of rewrite rules in a chemically intuitive manner that enable automatic abstraction of the level of detail in chemical pathways. Based on this rule composition we define an algorithmic framework for generation of vast reaction networks for specific spaces of a given chemistry, while still maintaining the level of detail of the model down to the atomic level. The framework also allows for computation with graphs and graph grammars, which is utilised to model non-trivial chemical systems. The graph generation relies on graph isomorphism testing, and we review the general individualisation-refinement paradigm used in the state-of-the-art algorithms for graph canonicalisation, isomorphism testing, and automorphism discovery. We present a model for chemical pathways based on a generalisation of network flows from ordinary directed graphs to directed hypergraphs. The model allows for reasoning about the flow of individual molecules in general pathways, and the introduction of chemically motivated routing constraints. It further provides the foundation for defining specialised pathway motifs, which is illustrated by defining necessary topological constraints for both catalytic and autocatalytic pathways. We also prove that central types of pathway questions are NP-complete, even for restricted classes of reaction networks. The complete pathway model, including constraints for catalytic and autocatalytic pathways, is implemented using integer linear programming. This implementation is used in a tree search method to enumerate both optimal and near-optimal pathway solutions. The formal methods are applied to multiple chemical systems: the enzyme catalysed beta-lactamase reaction, variations of the glycolysis pathway, and the formose process. In each of these systems we use rule composition to abstract pathways and calculate traces for isotope labelled carbon atoms. The pathway model is used to automatically enumerate alternative non-oxidative glycolysis pathways, and enumerate thousands of candidates for autocatalytic pathways in the formose process

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