On the hardness of solving edge matching puzzles as SAT or CSP problems

Edge matching puzzles have been amongst us for a long time now and traditionally they have been considered, both, a children’s game and an interesting mathematical divertimento. Their main characteristics have already been studied, and their worst-case complexity has been properly classified as a NP-complete problem. It is in recent times, specially after being used as the problem behind a money-prized contest, with a prize of 2US$ million for the first solver, that edge matching puzzles have attracted mainstream attention from wider audiences, including, of course, computer science people working on solving hard problems. We consider these competitions as an interesting opportunity to showcase SAT/CSP solving techniques when confronted to a real world problem to a broad audience, a part of the intrinsic, i.e. monetary, interest of such a contest. This article studies the NP-complete problem known as edge matching puzzle using SAT and CSP approaches for solving it. We will focus on providing, first and foremost, a theoretical framework, including a generalized definition of the problem. We will design and show algorithms for easy and fast problem instances generation, generators with easily tunable hardness. Afterwards we will provide with SAT and CSP models for the problems and we will study problem complexity, both typical case and worst-case complexity. We will also provide some specially crafted heuristics that result in a boost in solving time and study which is the effect of such heuristics.     

Bunsen section thermodynamic model for hydrogen production by the sulfur–iodine cycle

A model for the Bunsen section of the Sulfur–Iodine thermo-chemical cycle is proposed, where sulfur dioxide reacts with excess water and iodine to produce two demixing liquid aqueous phases (H₂SO₄ rich and HI rich) in equilibrium. Considering the mild temperature and pressure conditions, the UNIQUAC activity coefficient model combined with Engels' solvation model is used. The complete model is discussed, with HI solvation by water and by iodine as well as H₂SO₄ solvation by water, leading to a very high complexity with almost hundred parameters to be estimated from experimental data. Taking into account the water excess, a successful reduced model with only 15 parameters is proposed after defining new apparent species. Acids total dissociation and total H⁺ solvation by water are the main assumptions. Results show a good agreement with published experimental data between 25 °C and 120 °C.     

Countercurrent reactor design and flowsheet for iodine-sulfur thermochemical water splitting process

A conceptual design is presented for the I/S process for the production of hydrogen using a high-temperature nuclear heat source to split water. The process includes a countercurrent reactor being developed by CEA within the framework of an international collaboration (I-NERI project) with DOE at General Atomics (San Diego, CA). A ProsimPlus? model of the flowsheet indicates 600 kJ high-temperature heat and 69 kJ electric power are consumed per mole of H₂ product (with an assumed pressure of 120 bars). The net thermal efficiency would be 38% (HHV basis) if electric power is available at a conversion efficiency of 45%.     

HIx system thermodynamic model for hydrogen production by the Sulfur–Iodine cycle

The HI_x ternary system (H₂O–HI–I₂) is the latent source of hydrogen for the Sulfur–Iodine thermo-chemical cycle. After analysis of the literature data and models, a homogeneous approach with the Peng–Robinson equation of state used for both the vapor and liquid phase fugacity calculations is proposed for the first time to describe the phase equilibrium of this system. The MHV2 mixing rule is used, with UNIQUAC activity coefficient model combined with of hydrogen iodide solvation by water. This approach is theoretically consistent for HI_x separation processes operating above HI critical temperature. Model estimation is done on selected literature vapor–liquid, liquid–liquid, vapor–liquid–liquid and solid–liquid equilibrium data for the ternary system and the three binaries subsystems. Validation is done on the remaining literature data. Results agree well with the published data, but more experimental effort is needed to improve modeling of the HI_x system.     

A decision support system for coating selection based on fuzzy logic and multi-criteria decision making

Wear and corrosion are the most important factors that the surface of the engineering parts must confront. The need for protection and improvement of the mechanical characteristics of the surface of engineering parts can be to some extent satisfied by coatings. Coatings are considered as an excellent solution when resistance to corrosion, oxidation or low friction is demanded, but due the complexity of selecting the appropriate one, engineers often avoid them. The need for simultaneous consideration of qualitative and quantitative properties, render the use of classic material selection theories inadequate. An expert system for coating selection is presented in this paper, which can handle both qualitative and quantitative variables. The mathematical model used combines the multi-criteria decision making theories (MCDM) together with the fuzzy sets theory. The “Max-Min set” method is applied to calculate the ordering value of the alternatives while the TOPSIS method is used to rank them. A numerical example is provided to illustrate the method. Finally, the process presented can be easily computerized, to create the relative software.     

Data-driven and tool-supported elicitation of quality requirements in agile companies

Software Quality Journal - Quality requirements (QRs) are a key artifact needed to ensure the quality and success of a software system. Despite their importance, QRs rarely get the same degree of...     

Non-Linear Rewrite Closure and Weak Normalization

A rewrite closure is an extension of a term rewrite system with new rules, usually deduced by transitivity. Rewrite closures have the nice property that all rewrite derivations can be transformed into derivations of a simple form. This property has been useful for proving decidability results in term rewriting. Unfortunately, when the term rewrite system is not linear, the construction of a rewrite closure is quite challenging. In this paper, we construct a rewrite closure for term rewrite systems that satisfy two properties: the right-hand side term in each rewrite rule contains no repeated variable (right-linear) and contains no variable occurring at depth greater than one (right-shallow). The left-hand side term is unrestricted, and in particular, it may be non-linear. As a consequence of the rewrite closure construction, we are able to prove decidability of the weak normalization problem for right-linear right-shallow term rewrite systems. Proving this result also requires tree automata theory. We use the fact that right-shallow right-linear term rewrite systems are regularity preserving. Moreover, their set of normal forms can be represented with a tree automaton with disequality constraints, and emptiness of this kind of automata, as well as its generalization to reduction automata, is decidable. A preliminary version of this work was presented at LICS 2009 (Creus 2009).     

Biophysical and Computational Approaches to Study Ternary Complexes: A ‘Cooperative Relationship’ to Rationalize Targeted Protein Degradation

Degraders have illustrated that compound-induced proximity to E3 ubiquitin ligases can prompt the ubiquitination and degradation of disease-relevant proteins. Hence, this pharmacology is becoming a promising alternative and complement to available therapeutic interventions (e. g., inhibitors). Degraders rely on protein binding instead of inhibition and, hence, they hold the promise to broaden the druggable proteome. Biophysical and structural biology approaches have been the cornerstone of understanding and rationalizing degrader-induced ternary complex formation. Computational models have now started to harness the experimental data from these approaches with the aim to identify and rationally help design new degraders. This review outlines the current experimental and computational strategies used to study ternary complex formation and degradation and highlights the importance of effective crosstalk between these approaches in the advancement of the targeted protein degradation (TPD) field. As our understanding of the molecular features that govern drug-induced interactions grows, faster optimizations and superior therapeutic innovations for TPD and other proximity-inducing modalities are sure to follow.