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1. Defying Gravity and Gadget Numerosity: The Complexity of the Hanano Puzzle

   https://doi.org/10.1007/978-3-031-34326-1_3  

   Chavrimootoo, Michael C. (July 2023, Proceedings of the 25th International Conference on Descriptional Complexity of Formal Systems)

   Using the notion of visibility representations, our paper establishes a new property of in- stances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of reversible games with pushing blocks). Direct use of this property introduces an explosion in the number of gadgets needed to show PSPACE-hardness, but we show how to bring that number from 32 down to only three in general, and down to two in a specific case! We propose it as a step towards a broader and more general framework for studying games with irreversible gravity, and use this connection to guide an indirect polynomial-time many-one reduction from the NCL problem to the Hanano Puzzle—which is NP-hard—to prove it is in fact PSPACE-complete. 

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2. Synchronous Dynamical Systems on Directed Acyclic Graphs: Complexity and Algorithms

   https://doi.org/10.1145/3653723  

   Rosenkrantz, Daniel J; Marathe, Madhav V; Ravi, SS; Stearns, Richard E (June 2024, ACM Transactions on Computation Theory)

   Discrete dynamical systems serve as useful formal models to study diffusion phenomena in social networks. Several recent articles have studied the algorithmic and complexity aspects of some decision problems on synchronous Boolean networks, which are discrete dynamical systems whose underlying graphs are directed, and may contain directed cycles. Such problems can be regarded as reachability problems in the phase space of the corresponding dynamical system. Previous work has shown that some of these decision problems become efficiently solvable for systems on directed acyclic graphs (DAGs). Motivated by this line of work, we investigate a number of decision problems for dynamical systems whose underlying graphs are DAGs. We show that computational intractability (i.e.,PSPACE-completeness) results for reachability problems hold even for dynamical systems on DAGs. We also identify some restricted versions of dynamical systems on DAGs for which reachability problem can be solved efficiently. In addition, we show that a decision problem (namely, Convergence), which is efficiently solvable for dynamical systems on DAGs, becomesPSPACE-complete for Quasi-DAGs (i.e., graphs that become DAGs by the removal of asingleedge). In the process of establishing the above results, we also develop several structural properties of the phase spaces of dynamical systems on DAGs. 

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3. Optimal soft real-time semi-partitioned scheduling made simple (and dynamic)

   https://doi.org/10.1145/3356401.3356402  

   Hobbs, Clara; Tong, Zelin; Anderson, James H. (November 2019, Proceedings of the 27th International Conference on Real-Time Networks and Systems)

   Semi-partitioned scheduling is an approach to multiprocessor real-time scheduling where most tasks are fixed to processors, while a small subset of tasks is allowed to migrate. This approach offers reduced overhead compared to global scheduling, and can reduce processor capacity loss compared to partitioned scheduling. Prior work has resulted in a number of semi-partitioned scheduling algorithms, but their correctness typically hinges on a complex intertwining of offline task assignment and online execution. This brittleness has resulted in few proposed semi-partitioned scheduling algorithms that support dynamic task systems, where tasks may join or leave the system at runtime, and few that are optimal in any sense. This paper introduces EDF-sc, the first semi-partitioned scheduling algorithm that is optimal for scheduling (static) soft real-time (SRT) sporadic task systems and allows tasks to dynamically join and leave. The SRT notion of optimality provided by EDF-sc requires deadline tardiness to be bounded for any task system that does not cause over-utilization. In the event that all tasks can be assigned as fixed, EDF-sc behaves exactly as partitioned EDF. Heuristics are provided that give EDF-sc the novel ability to stabilize the workload to approach the partitioned case as tasks join and leave the system. 

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4. The Complexity of Iterated Reversible Computation

   https://doi.org/10.46298/theoretics.23.10  

   Eppstein, David (December 2023, TheoretiCS)

   We study a class of functional problems reducible to computing $$f^{(n)}(x)$$for inputs $$n$$ and $$x$$, where $$f$$ is a polynomial-time bijection. As we prove,the definition is robust against variations in the type of reduction used inits definition, and in whether we require $$f$$ to have a polynomial-time inverseor to be computible by a reversible logic circuit. These problems arecharacterized by the complexity class $$\mathsf{FP}^{\mathsf{PSPACE}}$$, andinclude natural $$\mathsf{FP}^{\mathsf{PSPACE}}$$-complete problems in circuitcomplexity, cellular automata, graph algorithms, and the dynamical systemsdescribed by piecewise-linear transformations. 

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5. Deciding Differential Privacy of Online Algorithms with Multiple Variables

   https://doi.org/10.1145/3576915.3623170  

   Chadha, Rohit; Sistla, A Prasad; Viswanathan, Mahesh; Bhusal, Bishnu (November 2023, ACM CCS '23: Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications Security)

   We consider the problem of checking the differential privacy of online randomized algorithms that process a stream of inputs and produce outputs corresponding to each input. This paper generalizes an automaton model called DiP automata [10] to describe such algorithms by allowing multiple real-valued storage variables. A DiP automaton is a parametric automaton whose behavior depends on the privacy budget ∈. An automaton A will be said to be differentially private if, for some D, the automaton is D∈-differentially private for all values of ∈ > 0. We identify a precise characterization of the class of all differentially private DiP automata. We show that the problem of determining if a given DiP automaton belongs to this class is PSPACE-complete. Our PSPACE algorithm also computes a value for D when the given automaton is differentially private. The algorithm has been implemented, and experiments demonstrating its effectiveness are presented. 

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