modularity of simple termination of term rewriting systems with shared constructors abstract kurihara m and a ohuchi modularity of simple termination of term rewriting systems with shared constructors theoretical computer science 103 1992 273 282 a term rewriting system is simply terminating if there exists a simplification ordering showing its termination let r and r be term rewriting systems which share no defined symbol but may share constructors constructors are function symbols which do not occur at the leftmost position in left hand sides of rewrite rules the rest of the function symbols are defined symbols in this paper we prove that r u r is simply terminating if and only if both r and r are so 1 introduction a property p of term rewriting systems trss 4 6 is modular if r u r has the property p if and only if both r0 and r have that property starting with toyama 141 several authors studied modular aspects of trss under the disjointness condition which requires that

on termination and confluence properties of disjoint and constructor sharing conditional rewrite systems abstract we investigate the modularity behavior of termination and confluence properties of join conditional term rewriting systems we give counterexamples showing that the properties weak termination weak innermost termination and strong innermost termination are not preserved in general under signature extensions then we develop sufficient conditions for the preservation of these properties under signature extensions and more generally for their modularity in the disjoint union case this leads to new criteria for modularity of termination and completeness generalizing known results for unconditional systems finally combining our analysis with recent related results on the preservation of semi completeness we show how to cover the non disjoint case of combined conditional rewrite systems with shared constructors too

grassmann extensions of yang baxter maps in this paper we show that there are explicit yang baxter yb maps with darboux lax representation between grassman extensions of algebraic varieties motivated by some recent results on noncommutative extensions of darboux transformations we first derive a darboux matrix associated with the grassmann extended derivative nonlinear schrodinger dnls equation and then we deduce novel endomorphisms of grassmann varieties which possess the yb property in particular we present ten dimensional maps which can be restricted to eight dimensional yb maps on invariant leaves related to the grassmann extended nls and dnls equations we consider their vector generalisations

saturated finite interval iterative learning for tracking of dynamic systems with hnn structural output this brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network hnn structural output the first objective is to design the output of a dynamic system with hnn structure a sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control ilc then the saturated ilc is considered into the discussed system and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique finally simulation results are given to illustrate the usefulness of the developed criteria

reduction groups and related integrable difference systems of nonlinear schrodinger type we extend the reduction group method to the lax darboux schemes associated with nonlinear schrodinger type equations we consider all possible finite reduction groups and construct corresponding lax operators darboux transformations hierarchies of integrable differential difference equations integrable partial difference systems and associated scalar partial difference equations

simple termination of rewrite systems abstract in this paper we investigate the concept of simple termination a term rewriting system is called simply terminating if its termination can be proved by means of a simplification order the basic ingredient of a simplification order is the subterm property but in the literature two different definitions are given one based on strict partial orders and another one based on preorders or quasi orders we argue that there is no reason to choose the second one as the first one has certain advantages simplification orders are known to be well founded orders on terms over a finite signature this important result no longer holds if we consider infinite signatures nevertheless well known simplification orders like the recursive path order are also well founded on terms over infinite signatures provided the underlying precedence is well founded we propose a new definition of simplification order which coincides with the old one based on partial orders in case of finite signatures but which is also well founded over infinite signatures and covers orders like the recursive path order we investigate the properties of the ensuing class of simply terminating systems

on the modularity of termination of term rewriting systems it is well known that termination is not a modular property of term rewriting systems i e it is not preserved under disjoint union the objective of this paper is to provide a uniform framework for sufficient conditions which ensure the modularity of termination we will prove the following result whenever the disjoint union of two terminating term rewriting systems is nonterminating then one of the systems is not ce terminating i e it loses its termination property when extended with the rules cons x y x and cons x y y and the other is collapsing this result has already been achieved by gramlich 7 for finitely branching term rewriting systems a more sophisticated approach is necessary however to prove it in full generality most of the known sufficient criteria for the preservation of termination 24 15 13 7 follow as corollaries from our result and new criteria are derived this paper particularly settles the open question whether simple termination is modular in general we will moreover shed some light on modular properties of combined systems with shared constructors for instance it will be shown that the above result does not carry over to constructor sharing systems

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

anticommutative extension of the adler map we construct a noncommutative grassmann extension of the well known adler yang baxter map it satisfies the yang baxter equation it is reversible and birational our extension preserves all the properties of the original map except the involutivity

explicit auto transformations of integrable chains a construction scheme for explicit auto transformations of integrable discrete differential equations chains is presented these transformations are rather convenient to obtain the exact solutions for chains as well as associated partial differential systems on the other hand they exemplify new integrable discrete mappings their group properties are also of great interest the scheme is illustrated by several examples of integrable systems which contains the nonlinear schrodinger system and the landau lifshits model

poisson yang baxter maps with binomial lax matrices a construction of multidimensional parametric yang baxter maps is presented the corresponding lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the sklyanin bracket these maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings an interesting family of quadrirational symplectic yb maps on c4 c4 with 3 3 lax matrices is also presented

integrable two component systems of difference equations we present two lists of two component systems of integrable difference equations defined on the edges of the z2 graph the integrability of these systems is manifested by their lax formulation whic

an inequality for the spectral radius of an interval matrix abstract for an n n interval matrix a aij we say that a is majorized by the point matrix a a ij if aij aij when the jth column of a has the property that there exists a power a m containing in the same jth column at least one interval not degenerated to a point interval and aij aij otherwise denoting the generalized spectral radius in the sense of daubechies and lagarias of a by a and the usual spectral radius of a by a it is proved that if a is majorized by a then a a this inequality sheds light on the asymptotic stability theory of discrete time linear interval systems

darboux transformations finite reduction groups and related yang baxter maps in this paper we construct yang baxter yb maps using darboux matrices which are invariant under the action of finite reduction groups we present six dimensional yb maps corresponding to darboux transformations for the nonlinear schrodinger nls equation and the derivative nonlinear schrodinger dnls equation these yb maps can be restricted to four dimensional yb maps on invariant leaves the former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries fordy a and kassotakis a 2013 j phys a math theor 46 205201 we give a six dimensional yb map corresponding to the darboux transformation for a deformation of the dnls equation we also consider vector generalizations of the yb maps corresponding to the nls and dnls equations

modularity in noncopying term rewriting it is known that termination and completeness are not modular properties of term rewriting systems the disjoint union of terminating complete term rewriting systems need not be terminating complete in this paper we introduce a class of noncopying term rewriting systems as a new term based formalism for a kind of graph rewriting systems and prove that this class enjoys the modularity of termination and of completeness actually our results are stronger in the sense that the disjointness condition is relaxed for allowing the systems to share constructors and some defined symbols while preserving the main results

on the convergence of powers of interval matrices abstract we give a necessary and sufficient condition for the sequence a k of the powers of an interval matrix a to converge to the null matrix o we construct a point matrix b which has spectral radius b less than one if a k converges

yang baxter maps with first degree polynomial 2 2 lax matrices a family of non parametric yang baxter yb maps is constructed by re factorization of 2 2 matrix polynomials of first degree these maps are poisson with respect to the sklyanin bracket for each casimir function a parametric poisson yb map is generated by reduction on the corresponding level set by considering a complete set of casimir functions symplectic multi parametric yb maps are derived these maps are quadrirational with explicit formulae in terms of matrix operations their lax matrices are by construction 2 2 first degree polynomial in the spectral parameter and are classified by the jordan normal form of the leading term degenerate parametric yb maps constructed as limits of the non degenerate ones are connected to known integrable systems on quadgraphs

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

on the church rosser property for the direct sum of term rewriting systems the direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols it is shown that if two term rewriting systems both have the chruch rosser property then the direct sum of these systems also has this property

iterative learning control for discrete time systems with event triggered transmission strategy and quantization this paper investigates the iterative learning problem for discrete time systems with event triggered scheme and quantization the event triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated here the event triggered scheme is designed depending on time t and iterative learning step k quantization is then introduced in the event triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties finally simulation results are given to illustrate the usefulness of the developed criteria

on the stability of discrete time linear interval systems abstract a general contraction mapping based method is proposed for studying the stability of linear interval systems sufficient conditions for the system uniform asymptotic stability using the products of vertex matrices are provided

brief paper stability analysis of discrete time iterative learning control systems with interval uncertainty this paper presents a stability analysis of the iterative learning control ilc problem for discrete time systems when the plant markov parameters are subject to interval uncertainty using the so called super vector approach to ilc vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ilc process it is shown that the stability of such interval ilc systems can be determined by checking the stability of the system using only the vertex points of the interval markov parameters

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

determinization of conditional term rewriting systems this paper discusses determinization of conditional term rewriting systems with oriented constructor rules we present a rule based transformation system which transforms a non deterministic one into a deterministic one together with examples of the transformation we prove that the transformation system is simulation sound and simulation complete we also prove that the transformation system is complete for some class by introducing a strategy for the transformation system

extreme point robust stability results for discrete time polynomials this paper provides some new extreme point robust stability results for discrete time polynomials with special uncertainties in the coefficient space the proofs obtained using the bilinear transformation are simple and the results specialize to existing robust stability results

yang baxter maps and symmetries of integrable equations on quad graphs a connection between the yang baxter relation for maps and the multidimensional consistency property of integrable equations on quad graphs is investigated the approach is based on the symmetry analysis of the corresponding equations it is shown that the yang baxter variables can be chosen as invariants of the multiparameter symmetry groups of the equations we use the classification results by adler bobenko and suris to demonstrate this method some new examples of yang baxter maps are derived in this way from multifield integrable equations

yang baxter maps and multi field integrable lattice equations a variety of yang baxter maps are obtained from integrable multi field equations on quad graphs a systematic framework for investigating this connection relies on the symmetry groups of the equations the method is applied to lattice equations introduced by adler and yamilov which are related to the nonlinear superposition formulae for the backlund transformations of the nonlinear schrodinger system and specific ferromagnetic models

exact maximum singular value of a complex interval matrix this paper shows that exact maximum singular value of a complex interval matrix can be found from a set of selected matrices the results include both square interval matrix and generalized non square interval matrix three illustrative examples are presented to verify the validity and utility of the proposed method

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

entwining yang baxter maps related to nls type equations we construct birational maps that satisfy the parametric set theoretical yang baxter equation and its entwining generalisation for this purpose we employ darboux transformations related to integrable nonlinear schrodinger type equations and study the refactorisation problems of the product of their associated darboux matrices additionally we study various algebraic properties of the derived maps such as invariants and associated symplectic or poisson structures and we prove their complete integrability in the liouville sense

integrable maps which preserve functions with symmetries we consider maps which preserve functions which are built out of the invariants of some simple vector fields we give a reduction procedure which can be used to derive commuting maps of the plane which preserve the same symplectic form and first integral we show how our method can be applied to some maps which have recently appeared in the context of yang baxter maps

a noncommutative discrete potential kdv lift in this paper we construct a grassmann extension of a yang baxter map which first appeared in the work of kouloukas and papageorgiou j phys a math theor 42 404012 2009 and can be considered as a lift of the discrete potential korteweg de vries dpkdv equation this noncommutative extension satisfies the yang baxter equation and it admits a 3 3 lax matrix moreover we show that it can be squeezed down to a novel system of lattice equations which possesses a lax representation and whose bosonic limit is the dpkdv equation finally we consider commutative analogs of the constructed yang baxter map and its associated quad graph system and we discuss their integrability

comments on convergence property of interval matrices and interval polynomials this note shows that the discrete linear interval system result of mori and kokame 1987 is also applicable to linear discrete time systems with linearly dependent perturbations

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem