We consider the problem of finding the smallest proof of unsatisfiability of a 2CNF formula. In particular, we look at Resolution refutations and at minimum unsatisfiable subsets of the clauses of the CNF. We give a characterization of minimum tree-like Resolution refutations that explains why, to find them, it is not sufficient to find shortest paths in the implication graph of the CNF. The ch...

The interest on quantum entanglement has dramatically increased during the last two decades due to the emerging field of quantum information theory [1, 2]. It turns out that quantum entanglement may be used as basic resources in quantum information processing and communication. The prominent examples are quantum cryptography, quantum teleportation, quantum error correction codes and quantum com...

We instrument a higher-order logic programming search procedure to generate and check small proof witnesses for the Twelf system, an implementation of the logical framework LF. In particular, we extend and generalize ideas from Necula and Rahul [16] in two main ways: 1) We consider the full fragment of LF including dependent types and higher-order terms and 2) We study the use of caching of sub...

Given a satisfiable 3-SAT formula, how hard is it to find an assignment to the variables that has Hamming distance at most n/2 to a satisfying assignment? More generally, consider any polynomial-time verifier for any NP-complete language. A d(n)-Hammingapproximation algorithm for the verifier is one that, given any member x of the language, outputs in polynomial time a string a with Hamming dis...

We construct entanglement witnesses using fundamental quantum operators of spin models which contain two-particle interactions and have a certain symmetry. By choosing the Hamiltonian as such an operator, our method can be used for detecting entanglement by energy measurement. We apply this method to the Heisenberg model in a cubic lattice with a magnetic field, the XY model and other familiar ...

If the witnesses of 19th-century civil marriages have been subject several researches, especially to distinguishing related and non-related witnesses, less attention has paid precise choice family members or witnesses. Even parents brides grooms, their presence absence at child's marriage, consequences on call friends The idea this article is provide new information about people who attend wedd...

Many witnesses to violent crimes are alcohol intoxicated, but research is lacking regarding how alcohol affects their perception of aggression and guilt. This study investigated to what extent alcohol intoxicated eyewitnesses differed from sober witnesses regarding how aggressive and guilty they perceived the involved parts in an intimate partner violence (IPV) situation. Eighty-seven healthy m...

In a celebrated paper, Valiant and Vazirani [29] raised the question of whether the difficulty of NP-complete problems was due to the wide variation of the number of witnesses of their instances. They gave a strong negative answer by showing that distinguishing between instances having zero or one witnesses is as hard as recognizing NP, under randomized reductions. We consider the same question...