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#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains… (More)

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality)… (More)

We extend the concept of a synchronizing word from finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i.e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it… (More)

We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its (1) downward closure, (2) upward closure, or (3) Parikh image. For the Parikh image over a fixed alphabet and for the… (More)

- UDC, D. V. Chistikov, S. E. Bubnov
- 2013

We prove a universal upper bound on checking test length for read-once functions over the elementary basis. We also identify the exact value of the corresponding Shannon function for the basis of conjunction and disjunction. A checking test problem for read-once functions, also known as testing with respect to read-once alternatives, was set up by A. A.… (More)

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. Restricted NMF requires in addition that the column spaces of M and W coincide. Finding the minimal inner dimension d is known to be NP-hard, both for NMF and restricted NMF.… (More)

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are… (More)

A checking test for a monotone read-once function f depending essentially on all its n variables is a set of vectors M distinguishing f from all other monotone read-once functions of the same variables. We describe an inductive procedure for obtaining individual lower and upper bounds on the minimal number of vectors T (f) in a checking test for any… (More)

We show that any one-counter automaton with n states, if its language is non-empty, accepts some word of length at most O(n 2). This closes the gap between the previously known upper bound of O(n 3) and lower bound of Ω(n 2). More generally, we prove a tight upper bound on the length of shortest paths between arbitrary configurations in one-counter… (More)

We determine the descriptional complexity (smallest number of states, up to constant factors) of recognizing languages {1 n } and {1 tn : t = 0, 1, 2,. . .} with state-based finite machines of various kinds. This task is understood as counting to n and modulo n, respectively, and was previously studied for classes of finite-state automata by Kupferman,… (More)