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We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
Partially ordered sets (posets) are fundamental combinatorial objects with important applications in computer science. Perhaps the most natural algorithmic task, given a size-$n$ poset, is to compute its number of linear extensions. In 1991…
Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer…
We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…
We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by D the largest absolute value of the subdeterminants of the constraint matrix. In this paper we…
In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Parikh's Theorem is a fundamental result in automata theory with numerous applications in computer science: software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic…
This paper presents two decidability results on the validity checking problem for entailments of symbolic heaps in separation logic with Presburger arithmetic and arrays. The first result is for a system with arrays and existential…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov…