Combinatorics and Probability

For the past few decades, Combinatorics and Probability Theory have had a fruitful symbiosis, each benefitting from and influencing developments in the other. Thus to prove the existence of designs, probabilistic methods are used, algorithms to factorize integers need combinatorics and probability theory (in addition to number theory), and the study of random matrices needs combinatorics. In the workshop a great variety of topics exemplifying this interaction were considered, including problems concerning designs, Cayley graphs, additive number theory, multiplicative number theory, noise sensitivity, random graphs, extremal graphs and random matrices

Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Optimisation of Definition Structures & Parameter Values in Process Algebra Models Using Evolutionary Computation

Process Algebras are a Formal Modelling methodology which are an effective tool for defining models of complex systems, particularly those involving multiple interacting processes. However, describing such a model using Process Algebras requires expertise from both the modeller and the domain expert. Finding the correct model to describe a system can be difficult. Further more, even with the correct model, parameter tuning to allow model outputs to match experimental data can also be both difficult and time consuming. Evolutionary Algorithms provide effective methods for finding solutions to optimisation problems with large and noisy search spaces. Evolutionary Algorithms have been proven to be well suited to investigating parameter fitting problems in order to match known data or desired behaviour. It is proposed that Process Algebras and Evolutionary Algorithms have complementary strengths for developing models of complex systems. Evolutionary Algorithms require a precise and accurate fitness function to score and rank solutions. Process Algebras can be incorporated into the fitness function to provide this mathematical score. Presented in this work is the Evolving Process Algebra (EPA) framework, designed for the application of Evolutionary Algorithms (specifically Genetic Algorithms and Genetic Programming optimisation techniques) to models described in Process Algebra (specifically PEPA and Bio-PEPA) with the aim of evolving fitter models. The EPA framework is demonstrated using multiple complex systems. For PEPA this includes the dining philosophers resource allocation problem, the repressilator genetic circuit, the G-protein cellular signal regulators and two epidemiological problems: HIV and the measles virus. For Bio-PEPA the problems include a biochemical reactant-product system, a generic genetic network, a variant of the G-protein system and three epidemiological problems derived from the measles virus. Also presented is the EPA Utility Assistant program; a lightweight graphical user interface. This is designed to open the full functionality and parallelisation of the EPA framework to beginner or naive users. In addition, the assistant program aids in collating and graphing after experiments are completed

Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)

International audienceOriginating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.This international conference “Algebras, graphs and ordered set” (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Maurice’s many scientific interests:• Lattices and ordered sets• Combinatorics and graph theory• Set theory and theory of relations• Universal algebra and multiple valued logic• Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics..