This paper is a continuation of the work begun in 5] on establishing relative intensional expressiveness results for programming languages. Language L 1 is intensionally more expressive than L 2 , if L 1 can compute all the functions L 2 can, with at least the same asymptotic complexity. The question we address is: Does nondeterministic parallelism add intensional expressiveness? We compare det...

Abstract In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal state and thermal-coherent state. use covariance matrix approach to calculate circuit complexity of states. approach, generate optimal geodesics by horizontal generator, using length minimal group manifold.

K. Y. Sill Information Systems Laboratory Stanford University Stanford, CA, 94305 T. Kailath Informat.ion Systems Laboratory Stanford U ni versity Stanford, CA, 94305 '~le introduce a geometric approach for investigating the power of threshold circuits. Viewing n-variable boolean functions as vectors in 'R'2", we invoke tools from linear algebra and linear programming to derive new results on t...

We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size dec...

Nielsen [3] recently asked the following question: ”What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation U , without the use of ancilla qubits?” Nielsen was able to prove that a lower bound on the minimal size circuit is provided by the length of the geodesic between the identity I and U , where the length is defined by a suitable Finsler ...

We use the techniques of Karchmer and Widgerson KW90] to derive strong lower bounds on the expected parallel time to compute boolean functions by circuits. By average time, we mean the time needed on a self-timed circuit, a model introduced recently by Jakoby, Reischuk, and Schindelhauer, JRS94] in which gates compute their output as soon as it is determined (possibly by a subset of the inputs ...

We show that all sets complete for NC1 under AC0 reductions are isomorphic under AC0computable isomorphisms. Although our proof does not generalize directly to other complexity classes, we do show that, for all complexity classes C closed under NC1-computable many-one reductions, the sets complete for C under NC0 reductions are all isomorphic under AC0-computable isomorphisms. Our result showin...

We present two simple and general techniques, both of which should find further application. First, we show that approximate compaction can be efficiently performed in constant parallel time using perfect hash functions. This allows us to show that polylogarithmic-threshold functions are in linear $AC^0$. Next, we show that the information theoretic notion of graph entropy captures some aspect ...