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On the Decidability of Membership in Matrix-exponential Semigroups
We consider the decidability of the membership problem for matrix-exponential semigroups: Given k∈ N and square matrices A1, … , Ak, C, all of the same dimension and with real algebraic entries, decide whether C is contained in the semigroup generated by ...
Near-optimal Linear Decision Trees for k-SUM and Related Problems
We construct near-optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant k, we construct linear decision trees that solve the k-SUM problem on n elements using O(n log2 n) ...
Parallel Bayesian Search with No Coordination
Coordinating the actions of agents (e.g., volunteers analyzing radio signals in SETI@home) yields efficient search algorithms. However, such an efficiency is often at the cost of implementing complex coordination mechanisms which may be expensive in ...
Uniform Sampling Through the Lovász Local Lemma
We propose a new algorithmic framework, called partial rejection sampling, to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds new connections between the variable framework ...
From Real-time Logic to Timed Automata
We show how to construct temporal testers for the logic MITL, a prominent linear-time logic for real-time systems. A temporal tester is a transducer that inputs a signal holding the Boolean value of atomic propositions and outputs the truth value of a ...
Shellability is NP-complete
We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, ...
Toward Verifying Nonlinear Integer Arithmetic
We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were ...
On the Computability of Conditional Probability
As inductive inference and machine-learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a universal ...
