Advances in String Algorithms and Computational Complexity

The field of string algorithms and computational complexity is rapidly advancing, with significant developments in decidability, query complexity, and recognition of languages. Recent research has focused on improving the efficiency of algorithms for solving complex problems, such as the not-contains string predicate and counting distinct substrings. Notably, innovative solutions have been proposed to tackle long-standing open questions, pushing the boundaries of what is considered computable. The study of query complexity under uncertainty has also led to important breakthroughs, including the development of hazard-free extensions of Boolean functions and improvements to decision tree constructions. In addition to these advances, researchers have made significant progress in understanding the relationships between different complexity classes, such as P^(#P) and the characterization of problems solvable by membrane systems with symport/antiport and membrane separation. Some particularly noteworthy papers include:

  • 'Negated String Containment is Decidable' which provides a positive answer to a long-standing open question,
  • 'Sensitivity and Query Complexity under Uncertainty' which proves an analogue of Huang's celebrated sensitivity theorem in a model of query complexity with uncertainty. These contributions demonstrate the field's growing ability to tackle complex problems and its increasing relevance to real-world applications, making it an exciting area of study for researchers and professionals alike.

Sources

Negated String Containment is Decidable (Technical Report)

Counting distinct (non-)crossing substrings

Translating between the representations of an acyclic convex geometry of bounded degree

Sensitivity and Query Complexity under Uncertainty

Eilenberg correspondence for Stone recognition

PANDAS: Peer-to-peer, Adaptive Networking for Data Availability Sampling within Ethereum Consensus Timebounds

Systemic Constraints of Undecidability

Asymptotic Preserving and Accurate scheme for Multiscale Poisson-Nernst-Planck (MPNP) system

Symport/Antiport P Systems with Membrane Separation Characterize P^(#P)

Optimality Loss Minimization in Distributed Control with Application to District Heating

Resolving CAP Through Automata-Theoretic Economic Design: A Unified Mathematical Framework for Real-Time Partition-Tolerant Systems

Responsibility Gap and Diffusion in Sequential Decision-Making Mechanisms

Built with on top of