Implementing tableaux by decision diagrams

Binary Decision Diagrams (BDDs) are usually thought of as devices engineered specially for classical propositional logic. We show that we can build on one of their variants, Minato\u27s zero-suppressed BDDs, to build compact data structures that encode whole tableaux. We call these structures tableaux decision diagrams (TDDs), and show how tableaux proof search is implemented in this framework. For this to be efficient, we have to restrict to canonical proof formats (in the sense of Galmiche et al.) to be able to take advantage of sharing in TDDs. Sharing is fundamental, not because it reduces memory consumption, but because it allows us to expand or close many tableaux paths in parallel, with corresponding gains in efficiency. We provide some empirical evidence that this is indeed efficient, by illustrating the method on a well-chosen system for propositional intuitionistic logic

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

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

Pain, sensation and biological responses following human skin puncture with microneedles

Future work should optimise the design of microneedle devices for clinical delivery of active molecules