decidable sentences of church rosser congruences abstract a decision procedure for a class of true sentences of congruences generated by finite monadic church rosser systems is developed using this decision procedure it is shown that if m t is the monoid presented by such a system t then i it is decidable given t whether m t is a group ii it is decidable given t and a finite set a whether the submonoid generated by a is a group or a left right two sided ideal and iii green s relations for m t are decidable

an extended direct branching algorithm for checking equivalence of deterministic pushdown automata abstract this paper extends the direct branching algorithm of 25 for checking equivalence of deterministic pushdown automata it does so by providing a technique called halting for dealing with nodes with unbounded degree in the comparison tree this may occur when a skipping step may be applied infinitely many times to a certain node as a result of infinite sequences of e moves this extension allows the algorithm to check equivalence of two deterministic pushdown automata when none of them is real time but in a certain condition that properly contains a case where one of them is real time strict

on language equations with invertible operations the paper studies language equations of the type x l r and l y r where l and r are given languages and is an invertible binary word language operation for most of the considered insertion and deletion operations the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular l and r in case l is a context free language and r is a regular one the existence of a solution is generally undecidable the results can be extended to more complex linear equations systems of linear equations as well as for equations of higher degree

prime phase retrieval via majorization minimization this paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown e g spectral components of a time sequence we develop low complexity algorithms with superior performance based on the majorization minimization mm framework the proposed algorithms are referred to as prime phase retrieval via the majorization minimization technique they are preferred to existing benchmark methods since at each iteration a simple surrogate problem is solved with a closed form solution that monotonically decreases the original objective function in total three algorithms are proposed using different majorization minimization techniques experimental results validate that our algorithms outperform existing methods in terms of successful recovery and mean square error under various settings

church rosser controlled rewriting systems and equivalence problems for deterministic context free languages we use a description of deterministic context free languages dcfl by a special type of church rosser rewriting systems to extend several procedures testing the equality of two languages in a subfamilyfof dcfl to procedures testing the equality of two languages one of which is inf the other beeing a general dcfl

on the knuth bendix completion for concurrent processes abstract we consider critical pairs for replacement systems over free partially commutative monoids this is done in order to apply the knuth bendix completion procedure to concurrent processes we will see that there are one rule systems which have no finite set of critical pairs therefore we develop a sufficient and computable condition such that finite trace replacement systems have a finite set of critical pairs this condition is always satisfied in the purely free case of semi thue systems or purely commutative case of vector replacement systems in fact it generalizes and unifies both cases we will give examples of how one can use this generalization

an efficient algorithm to decide whether a monoid presented by a regular church rosser thue system is a group abstract we give an o a 2 t algorithm that on the input of a regular church rosser thue system t on alphabet a decides whether or not the monoid m t presented by t is a group where a is the cardinality of a and t is the size of the thue system t in addition a problem is presented that is decidable for regular monadic church rosser thue systems but that is undecidable for finite non monadic church rosser thue systems

lambda confluence for context rewriting systems clearing restarting automata and limited context restarting automata are particular types of context rewriting systems a word w is accepted by such a system if there is a sequence of rewritings that reduces the word w to the empty word where each rewrite rule is extended by certain context conditions if each rewrite step is strictly length reducing as for example in the case of clearing restarting automata then the word problem for such a system can be solved nondeterministically in quadratic time if in addition the contextual rewritings happen to be confluent that is confluent on the congruence class of the empty word then the word problem can be solved deterministically in linear time here we show that confluence is decidable in polynomial time for limited context restarting automata of type r 2 but that this property is not even recursively enumerable for clearing restarting automata the latter follows from the fact that confluence is not recursively enumerable for finite factor erasing string rewriting systems

cancellation in context free languages enrichment by reduction the following problem is shown to be decidable given a context free grammar g and a string w x does there exist a string u l g such that w is obtained from u by deleting all substrings ui that are elements of the symmetric dyck set d 1 the intersection of any two context free languages can be obtained from only one context free language by cancellation either with the smaller semi dyck set d 1 d 1 or with d 1 itself also the following is shown here for the first time if the set eq xnx n n n d 1 is used for this cancellation then each recursively enumerable set can be obtained from linear context free languages previous work has shown that cancellation of substrings from the semi dyck language d 1 or from any of the former languages d 1 or eq allows one to obtain the following from the context free languages any terminal petri net language 14 16 the intersections of any context free with a terminal petri net language and the nested iterated substitution thereof 15 we generalize this characterization by showing that linear context free languages suffice for generating terminal petri net languages in proving this we obtain a new closure property of the family of petri net languages which is not shared by the context free sets

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

when is a monoid a group the church rosser case is tractable abstract the following question is shown to be tractable given a finite monadic church rosser thue system t and a finite set a is the submonoid generated by a of the monoid presented by t a group

canonical coset parametrization and the bures metric of the three level quantum systems an explicit parametrization for the state space of an n level density matrix is given the parametrization is based on the canonical coset decomposition of unitary matrices we also compute explicitly the bures metric tensor over the state space of two and three level quantum systems

rational subsets of partially reversible monoids a class of monoids that can model partial reversibility allowing simultaneously instances of two sided reversibility one sided reversibility and no reversibility is considered some of the basic decidability problems involving their rational subsets syntactic congruences and characterization of recognizability are solved using purely automata theoretic techniques giving further insight into the structure of recognizable languages

a direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata a new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata dpda s after korenjak and hopcroft s branching algorithm it is not only powerful enough to be applicable to two dpda s accepting by empty stack one of which is real time but also simple even for dpda s in lower subclasses this is the first time the branching algorithm has been used to give such a general decision procedure without ever mixing the two languages in question in other words it deals with only the equivalence equation whose left hand side consists of a pure reachable configuration of one dpda and whose right hand side that of the other

a polynomial time algorithm for deciding the equivalence problem for 2 tape deterministic finite state acceptors the equivalence problem for the class of one way deterministic 2 tape finite state acceptors is the problem of deciding l m 1 l m 2 where m 1 and m 2 are machines in this class a new algorithm for deciding equivalence is provided having time complexity proportional to p n where p is a polynomial and n is the size of the machines this improves upon the best previously known upper bound having order 2 cn 6 where c is a constant c beeri theoret comput sci 3 1976 pp 305 320

phase retrieval via wirtinger flow theory and algorithms we study the problem of recovering the phase from magnitude measurements specifically we wish to reconstruct a complex valued signal boldsymbol x in mathbb c n about which we have phaseless samples of the form y r left langle boldsymbol a r boldsymbol x rangle right 2 r 1 ldots m knowledge of the phase of these samples would yield a linear system this paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm in a nutshell this algorithm starts with a careful initialization obtained by means of a spectral method and then refines this initial estimate by iteratively applying novel update rules which have low computational complexity much like in a gradient descent scheme the main contribution is that this algorithm is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements indeed the sequence of successive iterates provably converges to the solution at a geometric rate so that the proposed scheme is efficient both in terms of computational and data resources in theory a variation on this scheme leads to a near linear time algorithm for a physically realizable model based on coded diffraction patterns we illustrate the effectiveness of our methods with various experiments on image data underlying our analysis are insights for the analysis of nonconvex optimization schemes that may have implications for computational problems beyond phase retrieval

phaseless near field far field transformation utilizing combinations of probe signals phaseless near field far field transformations based on nonconvex optimization suffer from local stationary points in order to avoid the corresponding suboptimal solutions the incorporation of combinations of probe signals into the cost functional is proposed and investigated the nonconvex optimization based on the wirtinger calculus relies on forward and adjoint radiation operator evaluations via the fast irregular antenna field transformation algorithm fiafta and is performed by a memory limited quasi newton method this allows the solution of large scale problems with utilization of the full flexibility of the fiafta in terms of measurement probe correction and arbitrary sample locations results for synthetic and measured near field data reveal significant improvements when the knowledge of probe signal combinations is utilized especially in applications with a large number of unknowns

monadic thue systems abstract certain infinite thue systems over a finite alphabet are studied in particular systems s e such that for each a e the set u u a s is a context freelanguage the syntactic structure of sets of ancestors and sets of descendants is considered as well as that of unions of congruence classes taken over infinite context free languages or regular sets the common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable even for finite systems the word problem for confluent systems of this type is shown to be tractable the question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

phaseless bi polar planar near field measurements and diagnostics of array antennas antenna near field measurements typically require very accurate measurement of the near field phase there are applications where an accurate phase measurement may not be practically achievable phaseless measurements are beginning to emerge as an alternative microwave antenna measurements technique when phase cannot be directly measured there are many important aspects for successful implementation of a phaseless measurement algorithm this paper presents appropriate phaseless measurement requirements and a phase retrieval algorithm tailored for the bi polar planar near field antenna measurement technique two amplitude measurements and a squared amplitude optimal sampling interpolation method are integrated with an iterative fourier procedure to first retrieve the phase information and then construct both the far field pattern and diagnostic characteristics of the antenna under test in order to critically examine the methodologies developed in this paper phaseless measurement results for two different array antennas are presented and compared to results obtained when the near field amplitude and phase are directly measured

erratum differential geometry on su 3 with applications to three state systems j math phys 39 6125 6136 1998 the first equation on page 6127 just above eq 2 is the equation for the right invariant vector fields not the left invariant vector fields this makes several sign changes in the appendices that we present here

sparse phase retrieval via truncated amplitude flow this paper develops a novel algorithm termed sparse truncated amplitude flow sparta to reconstruct a sparse signal from a small number of magnitude only measurements it deals with what is also known as sparse phase retrieval pr which is np hard in general and emerges in many science and engineering applications upon formulating sparse pr as an amplitude based nonconvex optimization task sparta works iteratively in two stages in stage one the support of the underlying sparse signal is recovered using an analytically well justified rule and subsequently a sparse orthogonality promoting initialization is obtained via power iterations restricted on the support and in the second stage the initialization is successively refined by means of hard thresholding based gradient type iterations sparta is a simple yet effective scalable and fast sparse pr solver on the theoretical side for any n dimensional k sparse k ll n signal boldsymbol x with minimum in modulus nonzero entries on the order of 1 sqrt k vert boldsymbol x vert 2 sparta recovers the signal exactly up to a global unimodular constant from about k 2 log n random gaussian measurements with high probability furthermore sparta incurs computational complexity on the order of k 2n log n with total runtime proportional to the time required to read the data which improves upon the state of the art by at least a factor of k finally sparta is robust against additive noise of bounded support extensive numerical tests corroborate markedly improved recovery performance and speedups of sparta relative to existing alternatives

some undecidability results concerning the property of preserving regularity a finite string rewriting system r preserves regularity if and only if it preserves regularity where is the alphabet containing exactly those letters that have occurrences in the rules of r this proves a conjecture of gyenizse and vagvolgyi 1997 in addition some undecidability results are presented that generalize results of gilleron and tison 1995 from term rewriting systems to string rewriting systems it follows that the property of being regularity preserving is undecidable for term rewriting systems thus answering another question of gyenizse and vagvolgyi 1997 finally it is shown that it is undecidable in general whether a finite lengthreducing and confluent string rewriting system yields a regular set of normal forms for each regular language

infinite regular thue systems abstract the following new results are obtained about infinite regular thue systems s 1 if s is church rosser the word problem is solvable in linear time 2 if s is monadic church rosser it defines a nontrivial boolean algebra of dcfls 3 if s is monadic church rosser and so is another system t equivalence of s and t is decidable 4 if s is monadic it is decidable if s is church rosser 5 if s is not monadic it is undecidable if s is church rosser

on regularity of context free languages this paper considers conditions under which a context free language is regular and conditions which imposed on productions of a rewriting system generating a context free language will guarantee that the generated language is regular in particular 1 1 necessary and sufficient conditions on productions of a unitary grammar are given that guarantee the generated language to be regular a unitary grammar is a semi thue system in which the left hand of each production is the empty word and 2 2 it is proved that commutativity of a linear language implies its regularity to obtain the former result we give a generalization of the myhill nerode characterization of the regular languages in terms of well quasi orders along with a generalization of higman s well quasi order result concerning the subsequence embedding relation on in obtaining the latter results we introduce the class of periodic languages and demonstrate how they can be used to characterize the commutative regular languages here we also utilize the theory of well quasi orders

a closure property of regular languages note given a semigroup homomorphism x p y where p y is the powerset of y we show that the inverse image k 1 of a regular set k y is regular too this theorem has several consequences generalizing previously known results

some decision problems about controlled rewriting systems abstract a description of deterministic context free languages by some kind of finitely generated right congruences the sets of relations generating such right congruences are called controlled rewriting systems or c systems has been given previously in the first part of this paper we study several decision problems on c systems namely the confluence problem the equivalence problem the refinement problem the class equivalence problem and the class inclusion problem in the second part of the paper we deduce from the main theorem given previously a characterisation of dcfls by means of finitely generated congruences the sets of relations generating such congruences are now ordinary finite semi thue systems we study three decision problems on finite semi thue systems namely the class equivalence problem the word problem for the syntactic congruence of one class and the partial confluence problem all the problems are investigated in several classes of c systems or semi thue systems for every class we give an answer which may be yes the problem is decidable no the problem is undecidable or eq which means that the problem is recursively equivalent to the equivalence problem for dpda

on the hamiltonian reduction of geodesic motion on su 3 to su 3 su 2 the reduced hamiltonian system on t su 3 su 2 is derived from a riemannian geodesic motion on the su 3 group manifold parametrized by the generalized euler angles and endowed with a bi invariant metric our calculations show that the metric defined by the derived reduced hamiltonian flow on the orbit space su 3 su 2 s5 is not isometric or even geodesically equivalent to the standard riemannian metric on the five sphere s5 embedded into r6

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

radiation pattern evaluation from near field intensities on planes this paper describes analyzes and implements an approach to far field determination from phaseless measurements over two planar surfaces a proper formulation of the problem is considered as a quadratic inverse one whose data is the square amplitude of the near field a solution is introduced as the global minimum of an appropriate functional next to perform such a minimization procedure a finite dimensional representation of the field radiated by sources whose plane wave spectrum becomes negligible outside a fixed angular domain is used a detailed investigation of the properties of the mapping connecting the unknowns to the data makes it possible to analyze how to escape from the local minima possibly met in the course of the minimization procedure to this end the crucial role of the availability of phaseless data over two different sarfa ces and of appropriate weights in the functional definition is emphasized and a reliable iterative procedure converging on the solution regardless of the starting point is thus obtained this property is confirmed by experimental results concerning near zone data from a shaped reflector at 9 ghz it can be readily appreciated that when only the field intensity is detected the complexity and the cost of the equipment required for near field techniques in antenna testing and diagnostics can be reduced to a very large extent

church rosser thue systems and formal languages since about 1971 much research has been done on thue systems that have properties that ensure viable and efficient computation the strongest of these is the church rosser property which states that two equivalent strings can each be brought to a unique canonical form by a sequence of length reducing rules in this paper three ways in which formal languages can be defined by thue systems with this property are studied and some general results about the three families of languages so determined are studied

on data increasing in phase retrieval via quadratic inversion flattening manifold and local minima in this article we address the question of traps in phase retrieval via quadratic inversion first we clarify the genesis of local minima from a geometrical perspective by showing how the shape of the manifold of data and the position of the data point are related to the presence of local minima in the objective functional later we recall a mathematical condition for the lack of traps afterward we illustrate how the ratio between the dimension of data space m and the number of real unknowns n r impacts on the manifold of data and consequently on the presence of local minima in particular we show that if the dimension of data space is high enough the manifold of data is sufficiently large and no traps appear in the functional in the last part of this article with reference to a particular unknown sequence we establish the minimum value of the ratio m n r such that no traps should appear in the functional in this condition phase retrieval via quadratic inversion exhibits a global convergence behavior consequently the actual solution of the problem can be reached regardless of the initial guess which can be chosen completely at random

on the equivalence problem for regular thue systems abstract a decision procedure is presented for the equivalence problem for regular almost confluent thue systems on the other hand the equivalence problem for regular preperfect systems is shown to be undecidable

complexity results on the conjugacy problem for monoids abstract the complexity of the conjugacy problem cp m for monoids given by presentations of the form t is investigated here t denotes a possibly infinite thue system over the alphabet the following results are obtained 1 1 if t is finite and church rosser then cp m is in n time n if in addition t is special then cp m is in p 2 2 if t is infinite and church rosser but of the form i i d i r 1 where i is finite and each d i is in np then cp m is in np however if i is infinite then cp m can be undecidable even if t is recursive 3 3 if t is finite and almost confluent then cp m can be decidable with any degree in the grzegorczyk hierarchy or it can be undecidable with any recursively enumerable degree of unsolvability

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

on a special monoid with a single defining relation abstract we show that no finite union of congruence classes w w being an arbitrary element of the free monoid a b with unit 1 is a context free language if the congruence is defined by the single pair abbaab 1 this congruence is neither confluent nor even preperfect the monoid formed by its congruence classes is a group which has infinitely many isomorphic proper subgroups

undecidable questions related to church rosser thue systems abstract the following four properties are shown undecidable for finite thue systems s is s equivalent to a finite church rosser respectively almost confluent preperfect system does s generate a church rosser congruence

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

undecidable properties of monoids with word problem solvable in linear time part ii cross sections and homological and homotopical finiteness conditions using a particular simulation of single tape turing machines by finite string rewriting systems the first two authors have shown that all linear markov properties are undecidable for the class of finitely presented monoids with linear time decidable word problem expanding on this construction it is shown here that also many properties that are not known to be linear markov properties are undecidable for this class of monoids these properties include the existence of context free or regular cross sections the existence of finite convergent presentations the property of being automatic and the homological and homotopical finiteness properties left and right fpn n 3 fht and fdt

undecidable properties of monoids with word problem solvable in linear time let c1 be the class of finitely presented monoids with word problem solvable in linear time let p be a markov property of monoids related to class c1 in some sense it is undecidable given a monoid in c1 whether it satisfies p let c and c be classes of finitely presented monoids with word problem solvable in some time bounds if c contains c1 and c properly contains c then it is undecidable given a monoid in c whether it belongs to c

phase retrieval using alternating minimization phase retrieval problems involve solving linear equations but with missing sign or phase for complex numbers information more than four decades after it was first proposed the seminal error reduction algorithm of gerchberg and saxton and fienup is still the popular choice for solving many variants of this problem the algorithm is based on alternating minimization i e it alternates between estimating the missing phase information and the candidate solution despite its wide usage in practice no global convergence guarantees for this algorithm are known in this paper we show that a resampling variant of this approach converges geometrically to the solution of one such problem finding a vector bf x from bf y bf a where bf y vert bf a t bf x vert and vert bf z vert denotes a vector of element wise magnitudes of bf z under the assumption that bf a is gaussian empirically we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem which are based on lifting to a convex matrix problem in sample complexity and robustness to noise however it is much more efficient and can scale to large problems analytically for a resampling version of alternating minimization we show geometric convergence to the solution and sample complexity that is off by log factors from obvious lower bounds we also establish close to optimal scaling for the case when the unknown vector is sparse our work represents the first theoretical guarantee for alternating minimization albeit with resampling for any variant of phase retrieval problems in the non convex setting

the equivalence problem for real time dpdas the equivalence problem for deterministic real time pushdown automata is shown to be decidable this result is obtained by showing that valiant s parallel stacking technique using a replacement function introduced in this paper succeeds for deterministic real time pushdown automata equivalence is also decidable for two deterministic pushdown automata one of which is real time

a characterisation of deterministic context free languages by means of right congruences we study here a kind of rewriting systems called controlled rewriting systems c systems for short which generalise the notion of regular semi thue systems we show that the deterministic context free languages are exactly the sets of the form r s where r is a rational set and s is the right congruence generated by a c system of s of a restricted type s is basic and confluent

mcnaughton families of languages in 1988 the church rosser languages were introduced by mcnaughton et al as those languages that are recognized by finite length reducing and confluent string rewriting systems using extra non terminal symbols here we generalize this concept by considering classes of languages that are obtained by other types of string rewriting systems to honour robert mcnaughton s original contribution we call the resulting families of languages mcnaughton families here it is shown that the concept of mcnaughton families is as powerful as the notion of turing machine or the notion of phrase structure grammar we investigate the relationships between the various mcnaughton families obtaining an extensive hierarchy of classes that includes many well known language and complexity classes as well as some new classes further we consider some closure and non closure properties for those mcnaughton families that are contained in the class of context free languages and we address the complexity of the fixed and the general membership problems for these families

a finitely presented monoid which has solvable word problem but has no regular complete presentation squier 1987 showed that there exist finitely presented monoids with solvable word problem which cannot be presented by finite complete rewriting systems in the present note we give a finitely presented monoid with solvable word problem which cannot be presented by a regular complete system we do not use the homological algebra as squier did first we show that if a monoid is presented by a regular complete system and has some property it has either polynomial or exponential growth next we construct a finitely presented monoid with intermediate growth which satisfies the desired properties

undersampled sparse phase retrieval via majorization minimization in the undersampled phase retrieval problem the goal is to recover an n dimensional complex valued signal from only m intensity measurements without phase information this inverse system is not only nonconvex but also underdetermined in this paper we propose to exploit the sparsity in the original signal and develop two low complexity algorithms with superior performance based on the majorization minimization framework the proposed algorithms are preferred to existing benchmark methods since at each iteration a simple convex surrogate problem is solved with a closed form solution that monotonically decreases the objective function value when the unknown signal is sparse in the standard basis the first algorithm c prime can produce a stationary point of the corresponding nonconvex phase retrieval problem when the unknown signal is not sparse in the standard basis the second algorithm sc prime can find a coordinatewise stationary point of the more challenging phase retrieval problem through sparse coding experimental results validate that the proposed algorithms have higher successful recovery rate and less normalized mean square error than existing up to date methods under the same setting

the bisimulation problem for equational graphs of finite out degree the bisimulation problem for equational graphs of finite out degree is shown to be decidable we reduce this problem to the eta bisimulation problem for deterministic rational vectors of boolean series on the alphabet of a deterministic pushdown automaton cal m we then exhibit a complete formal system for deducing equivalent pairs of such vectors

majorization minimization algorithms in signal processing communications and machine learning this paper gives an overview of the majorization minimization mm algorithmic framework which can provide guidance in deriving problem driven algorithms with low computational cost a general introduction of mm is presented including a description of the basic principle and its convergence results the extensions acceleration schemes and connection to other algorithmic frameworks are also covered to bridge the gap between theory and practice upperbounds for a large number of basic functions derived based on the taylor expansion convexity and special inequalities are provided as ingredients for constructing surrogate functions with the pre requisites established the way of applying mm to solving specific problems is elaborated by a wide range of applications in signal processing communications and machine learning

groups presented by finite two monadic church rosser thue systems it is shown that a group g can be defined by a monoid presentation of the form 2 7 where t is a finite two monadic church rosser thue system over 2 if and only if g is isomorphic to the free product of a finitely generated free group with a finite number of finite groups

an explicit computation of the bures metric over the space of n dimensional density matrices the aim of this paper is to provide a method for explicit computation of the bures metric over the space of n level quantum system based on the coset parametrization of density matrices

some undecidability results for non monadic church rosser thue systems abstract in this paper the computational power of finite church rosser thue systems that are non monadic is explored in particular it is shown that there exists a finite non monadic church rosser thue system t such that the set of linear sentences that are true under the interpretation given by t is undecidable this contrasts with the situation for finite church rosser thue systems that are monadic in addition some problems are presented that are decidable for finite monadic church rosser thue systems but that are undecidable in general for finite non monadic church rosser thue systems finally it is shown how degrees of complexity can be encoded in finite non monadic church rosser thue systems

phase recovery maxcut and complex semidefinite programming phase retrieval seeks to recover a signal x in mathbb c p x c p from the amplitude a x a x of linear measurements ax in mathbb c n a x c n we cast the phase retrieval problem as a non convex quadratic program over a complex phase vector and formulate a tractable relaxation called phasecut similar to the classical maxcut semidefinite program we solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in gerchberg and saxton optik 35 237 246 1972 where each iteration is a matrix vector product numerical results show the performance of this approach over three different phase retrieval problems in comparison with greedy phase retrieval algorithms and matrix completion formulations

elements of finite order for finite monadic church rosser thue systems a thue system t over z is said to allow nontrivial elements of finite order if there exist a word u e 2 and integers n 0 and k 1 such that u 9 tx

a frequency domain near field to far field transform for planar layered media we report a frequency domain near field to far field transform nffft for the numerical modeling of radiation and scattering in planar multilayered spaces although the results are equivalent to those of demarest 1996 the formulation is more compact more stable and applicable to observation angles in the lower half space furthermore the results are presented in a vector potential formalism that is more easily adaptable to existing free space implementations the nffft algorithm can be used in any differential equation based finite numerical method including but not limited to the finite difference time domain fdtd method and the finite element method fem

a polynomial algorithm testing partial confluence of basic semi thue systems we give a polynomial algorithm solving the problem is s partially confluent on the rational set r for finite basic noetherian semi thue systems the algorithm is obtained by a polynomial reduction of this problem to the equivalence problem for deterministic 2 tape finite automata which has been shown to be polynomially decidable in fri gre82

reductions in tree replacement systems abstract certain kinds of church rosser tree replacement systems reduction systems are studied most results presented here generalize results proved for string rewriting systems by book 1982 the concept of a tree rewriting system with a norm is introduced and studied a new tree reducing machine which reduces every input tree to an irreducible tree is defined as a consequence when the norm under consideration is the size of the tree the number of nodes the word problem for finite church rosser reduction systems is decidable in linear time in the size of the input tree church rosser monadic reduction systems generalizing the monadic thue systems of book 1982 and book et al 1982 are also studied it is shown that every congruence class and every finite union of congruence classes defined by such a system is accepted by a deterministic bottom up tree pushdown automation this new form of a tree automation is briefly studied

on the rational subset problem for groups we use language theory to study the rational subset problem for groups and monoids we show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups in particular it passes through free products amalgamated over finite subgroups and hnn extensions with finite associated subgroups we provide a simple proof of a result of grunschlag showing that the decidability of this problem is a virtual property we prove further that the problem is decidable for a direct product of a group g with a monoid m if and only if membership is uniformly decidable for g automaton subsets of m it follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort

phaselift exact and stable signal recovery from magnitude measurements via convex programming suppose we wish to recover a signal input amssym font abc cmmib10 def bi 1 hbox abc 1 bi x in bbb c n from m intensity measurements of the form that is from data in which phase information is missing we prove that if the vectors are sampled independently and uniformly at random on the unit sphere then the signal x can be recovered exactly up to a global phase factor by solving a convenient semidefinite program a trace norm minimization problem this holds with large probability provided that m is on the order of and without any assumption about the signal whatsoever this novel result demonstrates that in some instances the combinatorial phase retrieval problem can be solved by convex programming techniques finally we also prove that our methodology is robust vis a vis additive noise 2012 wiley periodicals inc

testing for the church rosser property abstract it is shown that there is a polynomial time algorithm to determine whether a finite thue system is church rosser