Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are — To the best of our knowledge — Particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems. Finally, the authors discuss open questions and propose an agenda for future work.

Dynamical Criticality: Overview and Open Questions

Boolean satisfiability (SAT) solvers are currently very effective in practice. However, there are still many challenging problems for SAT solvers. Nowadays, extra computational power is no longer coming from higher processor frequencies. At the same time, multicore architectures are becoming predominant. Exploiting this new architecture is essential for the evolution of SAT solvers. Due to the increasing interest in parallel SAT solving, it is important to give an overview of what has been done so far. This paper presents an overview of parallel SAT solving and it is expected to be a valuable document for researchers in this field. This overview covers the main topics of parallel SAT solving, namely, different approaches and a variety of clause sharing strategies. Additionally, an evaluation of multicore SAT solvers is presented, showing the evolution of multicore SAT solvers over the last years.

An overview of parallel SAT solving

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. In this paper we provide an overview of the works on dynamical criticality that are -to the best of our knowledge- particularly relevant for the criticality hypothesis. We review the main contributions concerning dynamics and information processing at the edge of chaos, and we illustrate the main achievements in the study of critical dynamics in biological systems. Finally, we discuss open questions and propose an agenda for future work.

Dynamical criticality: overview and open questions

The satisfiability problem in propositional logic (SAT) is the task to decide for a given propositional formula whether it has a model. This problem plays a prominent role in various areas of computer science, mathematical logic and artificial intelligence, but also in applications such as asynchronous circuit synthesis [29], inductive inference [41], integrity of databases [3], hardware verification and many others. SAT was also the first problem to be proven complete [11] and as such is amongst the central problems in theoretical computer science.

A review of the literature on local search algorithms for MAX-SAT

The past few years have seen enormous progress in the performance of propositional satisfiability (SAT) solvers, and consequently SAT solvers are widely used in industry for many applications. In spite of this progress, there is strong demand for higher SAT algorithms efficiency to solve harder and larger problems. Unfortunately, most modern solvers are sequential and fewer are parallel. Our intention is to review the work of this last decade on parallel resolution of SAT with DPLL solvers which are the most widely used complete ones.

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Andrea Roll

Papers

Criticality and Parallelism in GSAT