infinitary lambda calculus in a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems in this paper we perform the same task for the lambda calculus from the viewpoint of infinitary rewriting the bohm model of the lambda calculus can be seen as an infinitary term model in contrast to term rewriting there are several different possible notions of infinite term which give rise to different bohm like models which embody different notions of lazy or eager computation

a class of label correcting methods for the k shortest paths problem in this paper we deal with the problem of finding the firstk shortest paths from a single origin node to all other nodes of a directed graph in particular we define the necessary and sufficient conditions for a set of distance label vectors on the basis of which we propose a class of methods which can be viewed as an extension of the generic label correcting method for solving the classical single origin all destinations shortest path problem the data structure used is characterized by a set ofk lists of candidate nodes and the proposed methods differ in the strategy used to select the node to be extracted at each iteration the computational results show that 1 some label correcting methods are generally much faster than the double sweep method of shier 1979 2 the most efficient node selection strategies used for solving the classical single origin all destinations shortest path problem have proved to be effective also in the case of thek shortest paths

enhancing spl epsiv approximation algorithms with the optimal linear scaling factor finding a least cost path subject to a delay constraint in a network is an np complete problem and has been extensively studied many works reported in the literature tackle this problem by using epsiv approximation schemes and scaling techniques i e by mapping link costs into integers or at least discrete numbers a solution which satisfies the delay constraint and has a cost within a factor of the optimal one that can be computed with pseudopolynomial computational complexity in this paper having observed that the computational complexities of the epsiv approximation algorithms using the linear scaling technique are linearly proportional to the linear scaling factor we investigate the issue of finding the optimal the smallest linear scaling factor to reduce the computational complexities and propose two algorithms the optimal linear scaling algorithm olsa and the transformed olsa we analytically show that the computational complexities of our proposed algorithms are very low as compared with those of epsiv approximation algorithms therefore incorporating the two algorithms can enhance the epsiv approximation algorithms by granting them a practically important capability self adaptively picking the optimal linear scaling factors in different networks as such epsiv approximation algorithms become more flexible and efficient

some new results on easy lambda terms abstract given two closed terms a and b we consider the question whether the equation a b is consistent with the calculus in general the problem is undecidable however if a is a 0 term we can give good sufficient conditions for the consistency of a b this allows us to prove some counterintuitive results such as 1 there is a closed term x which can be consistently equated to every closed term with the exception of the identity 2 there is a closed term which can be consistently equated to every closed normal form but not to the curry fixed point operator y

set theoretical and other elementary models of the l calculus abstract part i pp 351 373 of this paper is the previously unpublished 1972 memorandum plotkin 1972 with editorial changes and some minor corrections part ii pp 373 409 presents what happened next together with some further development of the material the first part begins with an elementary set theoretical model of the calculus functions are modelled in a similar way to that normally employed in set theory by their graphs difficulties are caused in this enterprise by the axiom of foundation next based on that model a model of the calculus is constructed by means of a natural deduction method finally a theorem is proved giving some general properties of those nontrivial models of the calculus which are continuous complete lattices the second part begins with a brief discussion of models of the calculus in set theories with anti foundation axioms next the model of the calculus of part i and also the closely related but different models of scott 1976 1980 and of engeler 1981 1988 are reviewed then general frameworks in which elementary constructions of models can be given are discussed following longo 1982 one can employ certain scott engeler algebras following coppo et al 1983 one can obtain filter models from their extended applicative type structures an extended discussion is given of various ways of constructing models of the calculus and the connections between them finally an extension of the theorem to complete partial orders is given the theme of the paper is the consideration of means of constructing models there is hardly any analysis of their properties there is no discussion of their application

a graph theory approach to identify resonant and non resonant transmission paths in statistical modal energy distribution analysis statistical modal energy distribution analysis smeda extends classical statistical energy analysis sea to the mid frequency range by establishing power balance equations between modes in different subsystems this circumvents the sea requirement of modal energy equipartition and enables applying smeda to the cases of low modal overlap locally excited subsystems and to deal with complex heterogeneous subsystems as well yet widening the range of application of sea is done at a price with large models because the number of modes per subsystem can become considerable when the frequency increases therefore it would be worthwhile to have at one s disposal tools for a quick identification and ranking of the resonant and non resonant paths involved in modal energy transmission between subsystems it will be shown that previously developed graph theory algorithms for transmission path analysis tpa in sea can be adapted to smeda and prove useful for that purpose the case of airborne transmission between two cavities separated apart by homogeneous and ribbed plates will be first addressed to illustrate the potential of the graph approach a more complex case representing transmission between non contiguous cavities in a shipbuilding structure will be also presented

transform domain characterization of abelian codes abelian codes constitute a class of codes that includes cyclic codes as a special case it is shown that the general class of abelian codes can be characterized in the transform domain using the discrete fourier transform dft over finite fields with the appropriate mixed radix number system as the indexing scheme for dft coefficients a simple transform domain description for dual codes of abelian codes is also obtained using this description the idempotent generator of the dual of a given abelian code can be easily obtained finally it is shown that in the case of cyclic codes which can be considered as abelian codes also one can work in smaller extension fields compared to the extension fields if they were considered as cyclic codes only

a finite equational axiomatization of the functional algebras for the lambda calculus abstract a lambda theory satisfies an equation between contexts where a context is a term with some holes in it if all the instances of the equation fall within the lambda theory in the main result of this paper it is shown that the equations between contexts valid in every lambda theory have an explicit finite equational axiomatization the variety of algebras determined by the above equational theory is characterized as the class of isomorphic images of functional lambda abstraction algebras these are algebras of functions and naturally arise as the coordinatizations of environment models or lambda models the natural combinatory models of the lambda calculus the main result of this paper is also applied to obtain a completeness theorem for the infinitary lambda calculus recently introduced by berarducci

enumerating k best paths in length order in dags abstract we address the problem of finding the k best paths connecting a given pair of nodes in a directed acyclic graph dag with arbitrary lengths one of the main results in this paper is the proof that a tree representing the k th shortest path is obtained by an arc exchange in one of the previous k 1 trees each of which contains a previous best path an o m k n log k time and o k m space algorithm is designed to explicitly determine the k shortest paths in a dag with n nodes and m arcs the algorithm runs in o m kn time using o k m space in dags with integer length arcs empirical results confirming the superior performance of the algorithm to others found in the literature for randomly generated graphs are reported

constructing the nearly shortest path in crossed cubes a graph g is panconnected if each pair of distinct vertices u v v g are joined by a path of length l for all d g u v

a class of bounded functions a database language and an extended lambda calculus abstract we develop an approach of partial computations for the lambda calculus it produces a class of bounded functions i e the co domains are finite while the domains are possibly infinite including self applicable functions we show that the bounded functions are recursive and have to be represented as lambda terms without head normal form in the lambda calculus in parallel we develop a language independently from the lambda calculus it also represents the class of bounded functions and therefore can produce whatever a turing machine produces provided that computation has finite time and space we call such a language a database language because we can use the language to construct and query business objects in database practice with the bounded functions we are able to extend the lambda calculus to effectively reduce terms having weak head normal form in a manner similar to how the standard lambda calculus reduces terms that have normal form

graph easy sets of mute lambda terms among the unsolvable terms of the lambda calculus the mute ones are those having the highest degree of undefinedness in this paper we define for each natural number n an infinite and recursive set m n of mute terms and show that it is graph easy for any closed term t of the lambda calculus there exists a graph model equating all the terms of m n to t alongside we provide a brief survey of the notion of undefinedness in the lambda calculus

filter models for conjunctive disjunctive l calculi abstract the distinction between the conjunctive nature of non determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work calculus is extended with both a non deterministic choice and a parallel operator a notion of reduction is introduced extending reduction of the classical calculus we study type assignment systems for this calculus together with a denotational semantics which is initially defined constructing a set semimodel via simple types we enrich the type system with intersection and union types dually reflecting the disjunctive and conjunctive behaviour of the operators and we build a filter model the theory of this model is compared both with a morris style operational semantics and with a semantics based on a notion of capabilities

complete restrictions of the intersection type discipline abstract in this paper the intersection type discipline as defined in barendregt 1983 is studied we will present two different and independent complete restrictions of the intersection type discipline the first restricted system the strict type assignment system is presented in section 2 its major feature is the absence of the derivation rule and it is based on a set of strict types we will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in barendregt we will show that the strict type assignment system is the nucleus of the full system i e for every derivation in the intersection type discipline there is a derivation in which is used only at the very end finally we will prove that strict type assignment is complete for inference semantics the second restricted system is presented in section 3 its major feature is the absence of the type we will show that this system gives rise to a filter i model and that type assignment without is complete for the i calculus finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable

an efficient time and space k point to point shortest simple paths algorithm abstract we address the problem identifying the k best point to point simple paths connecting a given pair of nodes in a directed network with arbitrary lengths the main result in this paper is the proof that a path tree containing the kth point to point shortest simple path can be obtained by using one of the previous k 1 path trees containing each one of the previous k 1 best point to point shortest simple paths the proof implies that at most n single source shortest path computations re optimizations in a network with non negative length arcs are made in each iteration of the method in the optimistic case this strategy only needs o m time to compute the best neighbor associated with a path tree that is the second shortest simple path given a shortest simple path the algorithm runs in o k nf n m cmax time and uses o k m space to determine the k point to point shortest simple paths in a directed network with n nodes m arcs and maximum absolute length cmax here o f n m cmax is the best time needed to determine the shortest simple paths connecting a source node with any other non source node in a network with non negative length arcs we improve required space in yen s algorithm by a multiplicative factor of o n2 for each best solution moreover our algorithm runs in the optimistic case in o kf n m cmax time this affirmation is confirmed by an experimental study where o k shortest paths are used to determine the k point to point shortest simple paths in two versions of our algorithm

the minmax regret robust shortest path problem in a finite multi scenario model the robust shortest path problem is a network optimization problem that can be defined to deal with uncertainty of costs associated with the arcs of a network two models have been considered for the robust shortest path problem interval data and discrete data sets this work addresses the robust shortest path problem with a minmax regret objective function on a finite multi scenario model this problem consists in finding an optimal path in the sense that it has the minimum maximum deviation from the shortest one over all scenarios with this goal some properties of the problem and of its optimal solutions are derived these results allow to introduce three approaches a labeling algorithm an algorithm based on ranking loopless paths and a hybrid algorithm which ranks loopless paths in a suitable way to apply the early elimination of useless solutions the algorithms are tested on random networks and compared with a previous method for the same problem the obtained computational results are reported and discussed they show that the labeling and the hybrid approaches outperform the others

type theories normal forms and d lambda models abstract a non standard inverse limit model d is constructed which has a non hilbert post complete theory moreover in d a simple semantic characterization of normalizable terms is given these results are proved using the properties of a generalized type assignment system which yields a filter model barendregt coppo and dezani ciancaglini 1983 j symbolic logic 48 931 940 coppo dezani ciancaglini honsell and longo 1983 pp 241 262 logic colloquium 82 north holland amsterdam isomorphic to d the type assignment system is also proved complete with respect to an interpretation of types in the term model of equality based only on normalization properties as an application a class of maximal monoids of normalizable terms is characterized

a filter model for concurrent lambda calculus type free lazy lambda calculus is enriched with angelic parallelism and demonic nondeterminism call by name and call by value abstractions are considered and the operational semantics is stated in terms of a must convergence predicate we introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract

improving space efficiency with path length prediction for finding k shortest simple paths finding mbi k shortest simple paths in a directed graph is a fundamental problem in many engineering applications most existing algorithms such as yen s algorithm and its variants have polynomial worst case time complexity but their average case running time is very high the heuristic algorithm mps can run significantly faster in practice however it requires an excessive amount of memory space in this paper we provide a new heuristic algorithm that achieves high space efficiency while maintaining similar average case running time we first propose a sidetrack representation of path with which a path can be stored in mbi o bf 1 space we then show how to categorize a candidate path as either partial or complete and restrict the number of paths added to the queue in addition we provide an empirical equation that can very accurately predict the mbi k th shortest path length provided that a much smaller number of shortest paths have been found extensive experiments prove that our algorithm can achieve an mbi o n speedup in practice over yen s algorithm in comparison with mps it runs up to three times faster and uses less space by an order of magnitude

what is a model of the lambda calculus an elementary purely algebraic definition of model for the untyped lambda calculus is given this definition is shown to be equivalent to the natural semantic definition based on environments these definitions of model are consistent with and yield a completeness theorem for the standard axioms for lambda convertibility a simple construction of models for lambda calculus is reviewed the algebraic formulation clarifies the relation between combinators and lambda terms

consta abelian codes over galois rings we study n length consta abelian codes a generalization of the well known abelian codes and constacyclic codes over galois rings of characteristic p sup a where n and p are coprime a twisted discrete fourier transform dft is used to generalize transform domain results of abelian and constacyclic codes to consta abelian codes further we characterize consta abelian codes invariant under two kinds of monomials whose underlying permutations are effected by i multiplying the coordinates with a unit in the appropriate mixed radix representation of the coordinate positions and ii shifting the coordinates by t positions all the codes studied here belong to the class of quasi twisted codes which are known to contain some good codes we show that the dual of a consta abelian code invariant under the two monomials is also a consta abelian code closed under both monomials

unified approach fuzzy graph problems we present a taxonomy of fuzzy graphs that treats fuzziness in vertex existence edge existence edge connectivity and edge weight within that framework we formulate some standard graph theoretic problems shortest paths and minimum cut for fuzzy graphs using a unified approach distinguished by its uniform application of guiding principles such as the construction of membership grades via the ranking of fuzzy numbers the preservation of membership grade normalization and the collapsing of fuzzy sets of graphs into fuzzy graphs finally we provide algorithmic solutions to these problems with examples

hermitian self dual abelian codes hermitian self dual abelian codes in a group ring fq2 g where fq2 is a finite field of order q2 and g is a finite abelian group are studied using the well known discrete fourier transform decomposition for a semisimple group ring a characterization of hermitian self dual abelian codes in fq2 g is given together with an alternative proof of necessary and sufficient conditions for the existence of such a code in fq2 g i e there exists a hermitian self dual abelian code in fq2 g if and only if the order of g is even and q 2l for some positive integer l later on the study is further restricted to the case where f22l g is a principal ideal group ring or equivalently g a z2k with 2 a based on the characterization obtained the number of hermitian self dual abelian codes in f22l a z2k can be determined easily when a is cyclic this result answers an open problem of jia et al concerning hermitian self dual cyclic codes in many cases f22l a z2k contains a unique hermitian self dual abelian code the criteria for such cases are determined in terms of l and the order of a finally the distribution of finite abelian groups a such that a unique hermitian self dual abelian code exists in f22l a z2 is established together with the distribution of odd integers m such that a unique hermitian self dual cyclic code of length 2 m over f22l exists

easiness in graph models we generalize baeten and boerboom s method of forcing to show that there is a fixed sequence uk k of closed untyped terms satisfying the following properties a for any countable sequence gk k of scott continuous functions of arbitrary arity on the power set of an arbitrary countable set there is a graph model such that x xx x xx uk represents gk in the model b for any countable sequence tk k of closed terms there is a graph model that satisfies x xx x xx uk tk for all k we apply these two results which are corollaries of a unique theorem to prove the existence of 1 a finitely axiomatized theory l such that the interval lattice constituted by the theories extending l is distributive 2 a continuum of pairwise inconsistent graph theories theories that can be realized as theories of graph models 3 a congruence distributive variety of combinatory algebras lambda abstraction algebras respectively

intersection types and domain operators we use intersection types as a tool for obtaining models relying on the notion of easy intersection type theory we successfully build a model in which the interpretation of an arbitrary simple easy term is any filter which can be described by a continuous predicate this allows us to prove two results the first gives a proof of consistency of the theory where the term x xx x xx is forced to behave as the join operator this result has interesting consequences on the algebraic structure of the lattice of theories the second result is that for any simple easy term there is a model where the interpretation of the term is the minimal fixed point operator

a generalized dft for abelian codes over z sub m a generalized discrete fourier transform defined over an appropriate extension ring is given that is suitable to characterize abelian codes over residue class integer rings z sub m the characterization is in terms of generalized discrete fourier transform components taking values from certain ideals of the extension ring it is shown that the results known for cyclic codes over z sub m like the simple characterization of dual and self dual codes and the nonexistence of self dual codes for certain values of code parameters extend to abelian codes over z sub m as well

abelian codes over galois rings closed under certain permutations we study n length abelian codes over galois rings with characteristic p sup a where n and p are relatively prime having the additional structure of being closed under the following two permutations i permutation effected by multiplying the coordinates with a unit in the appropriate mixed radix representation of the coordinate positions and ii shifting the coordinates by t positions a code is t quasi cyclic t qc if t is an integer such that cyclic shift of a codeword by t positions gives another codeword we call the abelian codes closed under the first permutation as unit invariant abelian codes and those closed under the second as quasi cyclic abelian qca codes using a generalized discrete fourier transform gdft defined over an appropriate extension of the galois ring we show that unit invariant abelian and qca codes can be easily characterized in the transform domain for t 1 qca codes coincide with those that are cyclic as well as abelian the number of such codes for a specified size and length is obtained and we also show that the dual of an unit invariant t qca code is also an unit invariant t qca code unit invariant abelian hence unit invariant cyclic and t qca codes over galois field f sub p sup l and over the integer residue rings are obtainable as special cases

a disambiguation algorithm for weighted automata abstract we present a disambiguation algorithm for weighted automata the algorithm admits two main stages a pre disambiguation stage followed by a transition removal stage we give a detailed description of the algorithm and the proof of its correctness the algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semiring by introducing the weak twins property in particular the algorithm can be used with any weighted automaton over the tropical semiring for which the weighted determinization algorithm terminates and with any acyclic weighted automaton over an arbitrary weakly left divisible cancellative and commutative semiring while disambiguation can sometimes be achieved using weighted determinization our disambiguation algorithm in some cases can return a result that is exponentially smaller than any equivalent deterministic automaton we also present some empirical evidence of the space benefits of disambiguation over determinization in speech recognition and machine translation applications

the labeled multi bernoulli filter this paper proposes a generalization of the multi bernoulli filter called the labeled multi bernoulli filter that outputs target tracks moreover the labeled multi bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi bernoulli filter by exploiting the conjugate prior form for labeled random finite sets the proposed filter can be interpreted as an efficient approximation of the delta generalized labeled multi bernoulli filter it inherits the advantages of the multi bernoulli filter in regards to particle implementation and state estimation it also inherits advantages of the delta generalized labeled multi bernoulli filter in that it outputs labeled target tracks and achieves better performance

on sets of solutions to combinator equations abstract we show that every r e set of combinators closed under conversion is the set of solutions to a pattern matching problem

transfinite reductions in orthogonal term rewriting systems strongly convergent reduction is the fundamental notion of reduction in infinitary orthogonal term rewriting systems otrss for these we prove the transfinite parallel moves lemma and the compressing lemma strongness is necessary as shown by counterexamples normal forms which we allow to be infinite are unique in contrast to normal forms strongly converging fair reductions result in normal forms

finding multi constrained multiple shortest paths numerous algorithms have been proposed for the well known multi constrained shortest path mcsp problem but very few have good practical performance in case of two or more constraints in this paper we propose a new lagrangian relaxation algorithm to solve a generalized version of the mcsp problem where we search for multiple shortest paths subject to multiple constraints as in some related work our algorithm first identifies the lower and upper bounds and then tries to close the gap with a path enumeration procedure however our algorithm is based on the recognition that the lagrange multipliers found by existing methods usually do not give the best search direction for minimizing path enumerations even though they can provide near optimized lower bounds we provide a solution to meet both of these goals and incorporate feasibility checks into a state of the art k shortest paths algorithm to further reduce path enumerations through experiments on various networks including the most challenging benchmark instances we show that our algorithm can solve a significantly larger number of instances to optimality with less computational cost often by one or two orders of magnitude when compared with the best known algorithm in the literature

on the k shortest simple paths problem in weighted directed graphs we present the first approximation algorithm for finding the k shortest simple paths connecting a pair of vertices in a weighted directed graph that breaks the barrier of mn it is deterministic and has a running time of o k m sqrt n n 3 2 log n where m is the number of edges in the graph and n is the number of vertices let s t in v the length of the i th simple path from s to t computed by our algorithm is at most frac 3 2 times the length of the i th shortest simple path from s to t the best algorithms for computing the exact k shortest simple paths connecting a pair of vertices in a weighted directed graph are due to yen management sci 17 1970 1971 pp 712 716 and lawler management sci 18 1971 1972 pp 401 405 the running time of their algorithms using modern data structures is o k mn n 2 log n both algorithms are from the early 70s although this problem and other variants of the k shortest path problem has drawn a lot of attention during the last three and a half decades the o k mn n 2 log n bound is still unbeaten

multiple path selection for new highway alignments using discrete algorithms abstract this paper addresses the problem of finding multiple near optimal spatially dissimilar paths that can be considered as alternatives in the decision making process for finding optimal corridors in which to construct a new road we further consider combinations of techniques for reducing the costs associated with the computation and increasing the accuracy of the cost formulation numerical results for five algorithms to solve the dissimilar multipath problem show that a bidirectional approach yields the fastest running times and the most robust algorithm further modifications of the algorithms to reduce the running time were tested and it is shown that running time can be reduced by an average of 56 percent without compromising the quality of the results

transducing markov sequences a markov sequence is a basic statistical model representing uncertain sequential data and it is used within a plethora of applications including speech recognition image processing computational biology radio frequency identification rfid and information extraction the problem of querying a markov sequence is studied under the conventional semantics of querying a probabilistic database where queries are formulated as finite state transducers specifically the complexity of two main problems is analyzed the first problem is that of computing the confidence probability of an answer the second is the enumeration of the answers in the order of decreasing confidence with the generation of the top k answers as a special case or in an approximate order thereof in particular it is shown that enumeration in any subexponential approximate order is generally intractable even for some fixed transducers and a matching upper bound is obtained through a proposed heuristic due to this hardness a special consideration is given to restricted yet common classes of transducers that extract matches of a regular expression subject to prefix and suffix constraints and it is shown that these classes are indeed significantly more tractable

choquet based optimisation in multiobjective shortest path and spanning tree problems this paper is devoted to the search of choquet optimal solutions in finite graph problems with multiple objectives the choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives we first present a condition on preferences name hereafter preference for interior points that characterizes preferences favouring compromise solutions a natural attitude in various contexts such as multicriteria optimisation robust optimisation and optimisation with multiple agents within choquet expected utility theory this condition amounts to using a submodular capacity and a convex utility function under these assumptions we focus on the fast determination of choquet optimal paths and spanning trees after investigating the complexity of these problems we introduce a lower bound for the choquet integral computable in polynomial time then we propose different algorithms using this bound either based on a controlled enumeration of solutions ranking approach or an implicit enumeration scheme branch and bound finally we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes

k a heuristic search algorithm for finding the k shortest paths we present a directed search algorithm called k for finding the k shortest paths between a designated pair of vertices in a given directed weighted graph k has two advantages compared to current k shortest paths algorithms first k operates on the fly which means that it does not require the graph to be explicitly available and stored in main memory portions of the graph will be generated as needed second k can be guided using heuristic functions we prove the correctness of k and determine its asymptotic worst case complexity when using a consistent heuristic to be the same as the state of the art o m nlogn k with respect to both runtime and space where n is the number of vertices and m is the number of edges of the graph we present an experimental evaluation of k by applying it to route planning problems as well as counterexample generation for stochastic model checking the experimental results illustrate that due to the use of heuristic on the fly search k can use less time and memory compared to the most efficient k shortest paths algorithms known so far

the shortest path problem with forbidden paths we consider a variant of the constrained shortest path problem where the constraints come from a set of forbidden paths arc sequences that cannot be part of any feasible solution two solution approaches are proposed for this variant the first uses aho and corasick s keyword matching algorithm to filter paths produced by a k shortest paths algorithm the second generalizes martins deviation path approach for the k shortest paths problem by merging the original graph with a state graph derived from aho and corasick s algorithm like martins approach the second method amounts to a polynomial reduction of the shortest path problem with forbidden paths to a classic shortest path problem its significant advantage over the first approach is that it allows considering forbidden paths in more general shortest path problems such as the shortest path problem with resource constraints

abelian codes in principal ideal group algebras we study abelian codes in principal ideal group algebras pigas we first give an algebraic characterization of abelian codes in any group algebra and provide some general results for abelian codes in a piga which can be viewed as cyclic codes over a semisimple group algebra it is shown that every abelian code in a piga admits generator and check elements these are analogous to the generator and parity check polynomials of cyclic codes a characterization and an enumeration of euclidean self dual and euclidean self orthogonal abelian codes in a piga are given which generalize recent analogous results for self dual cyclic codes in addition the structures of reversible and complementary dual abelian codes in a piga are established again extending results on reversible and complementary dual cyclic codes finally asymptotic properties of abelian codes in a piga are studied an upper bound for the minimum distance of abelian codes in a non semisimple piga is given in terms of the minimum distance of abelian codes in semisimple group algebras abelian codes in a non semisimple piga are then shown to be asymptotically bad similar to the case of repeated root cyclic codes

on the k shortest path trees problem abstract we address the problem of finding the k best path trees connecting a source node with any other non source node in a directed network with arbitrary lengths the main result in this paper is the proof that the k th shortest path tree is adjacent to at least one of the previous k 1 shortest path trees consequently we design an o f n m c max km time and o k m space algorithm to determine the k shortest path trees in a directed network with n nodes m arcs and maximum absolute length c max where o f n m c max is the best time needed to solve the shortest simple paths connecting a source node with any other non source node

efficient algorithms for learning functions with bounded variation we show that the class fbv of 0 1 valued functions with total variation at most 1 can be agnostically learned with respect to the absolute loss in polynomial time from o 1 e2 log 1 examples matching a known lower bound to within a constant factor we establish a bound of o 1 m on the expected error of a polynomial time algorithm for learning fbv in the prediction model also matching a known lower bound to within a constant factor applying a known algorithm transformation to our prediction algorithm we obtain a polynomial time pac learning algorithm for fbv with a sample complexity bound of o 1 e log 1 this also matches a known lower bound to within a constant factor

characterization theorems for a filter lambda model the filter model is a model of the calculus based on a system of type assignment which extends the basic functionality theory of curry invented in order to give a completeness proof for scott s semantics of curry s type assignment in this paper the local structure of this model i e the syntactical characterization of the equality and inclusion relation is given

quasi cyclic dyadic codes in the walsh hadamard transform domain a code is s quasi cyclic s qc if there is an integer s such that cyclic shift of a codeword by s positions is also a codeword for s 1 cyclic codes are obtained a dyadic code is a code which is closed under all dyadic shifts an s qc dyadic s qcd code is one which is both s qc and dyadic qcd codes with s 1 give codes that are cyclic and dyadic cd we obtain a simple characterization of all qcd codes hence of cd codes over any field of odd characteristic using walsh hadamard transform defined over that finite field also it is shown that dual a code of an s qcd code is also an s qcd code and s qcd codes for a given dimension are enumerated for all possible values of s

efficient calculation of the most reliable pair of link disjoint paths in telecommunication networks abstract in transmission networks an important routing problem is to find a pair of link disjoint paths which optimises some performance measure in this paper the problem of obtaining the most reliable pair of link disjoint paths assuming the reliability of the links are known is considered this is a non linear optimisation problem it is further introduced the constraint that the length of the paths should not exceed a certain number of links which makes the efficient resolution of the problem more complex in this paper two variants of a novel exact algorithm for finding the most reliable pair of link disjoint paths with lengths constraints are presented also a computational study on the performance of the variants is described

a bicriterion shortest path algorithm abstract among the network models one of the more popular is the so called shortest path problem this model is used whenever it is intended to minimize a linear function which represents a distance between a predetermined pair of nodes in a given network often a single objective function is not sufficient to completely characterize some real world problems for instance in a road network two parameters as cost and time can be assigned to each arc clearly the fastest path may be too costly nevertheless the decision maker must choose one solution possibly not the best for both criteria in this paper we present an algorithm for this problem with this algorithm a special set of paths the set of pareto optimal paths is determined one objective for any pareto optimal path can not be improved without worsening the other one

fast computation of bounds for two terminal network reliability in this paper an algorithm for the fast computation of network reliability bounds is proposed the evaluation of the network reliability is an intractable problem for very large networks and hence approximate solutions based on reliability bounds have assumed importance the proposed bounds computation algorithm is based on an efficient bdd representation of the reliability graph model and a novel search technique to find important minpaths mincuts to quickly reduce the gap between the reliability upper and lower bounds furthermore our algorithm allows the control of the gap between the two bounds by controlling the overall execution time therefore a trade off between prediction accuracy and computational resources can be easily made in our approach the numerical results are presented for large real example reliability graphs to show the efficacy of our approach

subcubic equivalences between path matrix and triangle problems we say an algorithm on n n matrices with integer entries in l m mr or n node graphs with edge weights from l m m is truly subcubic if it runs in o n3 poly log m time for some 0 we define a notion of subcubic reducibility and show that many important problems on graphs and matrices solvable in o n3 time are equivalent under subcubic reductions namely the following weighted problems either all have truly subcubic algorithms or none of them do the all pairs shortest paths problem on weighted digraphs apsp detecting if a weighted graph has a triangle of negative total edge weight listing up to n2 99 negative triangles in an edge weighted graph finding a minimum weight cycle in a graph of non negative edge weights the replacement paths problem on weighted digraphs finding the second shortest simple path between two nodes in a weighted digraph checking whether a given matrix defines a metric verifying the correctness of a matrix product over the min semiring finding a maximum subarray in a given matrix therefore if apsp cannot be solved in n3 e time for any e 0 then many other problems also need essentially cubic time in fact we show generic equivalences between matrix products over a large class of algebraic structures used in optimization verifying a matrix product over the same structure and corresponding triangle detection problems over the structure these equivalences simplify prior work on subcubic algorithms for all pairs path problems since it now suffices to give appropriate subcubic triangle detection algorithms other consequences of our work are new combinatorial approaches to boolean matrix multiplication over the or and semiring abbreviated as bmm we show that practical advances in triangle detection would imply practical bmm algorithms among other results building on our techniques we give two improved bmm algorithms a derandomization of the combinatorial bmm algorithm of bansal and williams focs 09 and an improved quantum algorithm for bmm

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

non existent statman s double fixed point combinator does not exist indeed we give a negative answer to a problem of r statman concerning the existence in the lambda calculus of a fixed point combinatorysuch thaty si yholds

heuristic methods for delay constrained least cost routing using spl kappa shortest paths the delay constrained least cost dclc problem is to find the least cost path in a graph subject to a delay constraint first formulated in the context of routing in computer networks the dclc model also applies to problems of path planning and other decision problems dclc is np complete many heuristic methods have been proposed for it this note presents two new methods based on the spl kappa shortest path spl kappa sp approach these heuristic methods one centralized the other distributed are both polynomial in numerical experiments the proposed algorithms almost always find the optimal paths

shortest path games abstract we study cooperative games that arise from the problem of finding shortest paths from a specified source to all other nodes in a network such networks model among other things efficient development of a commuter rail system for a growing metropolitan area we motivate and define these games and provide reasonable conditions for the corresponding rail application we show that the core of a shortest path game is nonempty and satisfies the given conditions but that the shapley value for these games may lie outside the core however we show that the shortest path game is convex for the special case of tree networks and we provide a simple polynomial time formula for the shapley value in this case in addition we extend our tree results to the case where users of the network travel to nodes other than the source finally we provide a necessary and sufficient condition for shortest paths to remain optimal in dynamic shortest path games where nodes are added to the network sequentially over time

combination of piecewise geodesic paths for interactive segmentation minimum cost paths have been extensively studied theoretical tools for interactive image segmentation the existing geodesically linked active contour glac model which basically consists of a set of vertices connected by paths of minimal cost blends the benefits of minimal paths and region based active contours this results in a closed piecewise smooth curve over which an edge or region energy functional can be formulated as an important shortcoming the glac in its initial formulation does not guarantee the curve to be simple consistent with respect to the purpose of segmentation in this paper we draw our inspiration from the glac and other boundary based interactive segmentation algorithms in the sense that we aim to extract a contour given a set of user provided points by connecting these points using paths the key idea is to select a combination among a set of possible paths such that the resulting structure represents a relevant closed curve instead of considering minimal paths only we switch to a more general formulation which we refer to as admissible paths these basically correspond to the roads travelling along the bottom of distinct valleys between given endpoints we introduce a novel term to favor the simplicity of the generated contour as well as a local search method to choose the best combination among possible paths

infinite l calculus and types recent work on infinitary versions of the lambda calculus has shown that the infinite lambda calculus can be a useful tool to study the unsolvable terms of the classical lambda calculus working in the framework of the intersection type disciplines we devise a type assignment system such that two terms are equal in the infinite lambda calculus iff they can be assigned the same types in any basis a novel feature of the system is the presence of a type constant to denote the set of all terms of order zero and the possibility of applying a type to another type we prove a completeness and an approximation theorem for our system our results can be considered as a first step towards the goal of giving a denotational semantics for the lambda calculus which is suited for the study of the unsolvable terms however some noncontinuity phenomena of the infinite lambda calculus make a full realization of this idea namely the construction of a filter model a quite difficult task

on the jacopini technique the general concern of the jacopini technique is the question is it consistent to extend a given lambda calculus with certain equations the technique was introduced by jacopini in 1975 in his proof that in the untyped lambda calculus omega is easy i e omega can be assumed equal to any other closed term without violating the consistency of the lambda calculus the presentations of the jacopini technique that are known from the literature are difficult to understand and hard to generalise in this paper we generalise the jacopini technique for arbitrary lambda calculi we introduce the concept of proof replaceability by which the structure of the technique is simplified considerably we illustrate the simplicity and generality of our formulation of the technique with some examples we apply the jacopini technique to the lambda mu calculus and we prove a general theorem concerning the consistency of extensions of the lambda mu calculus of a certain form many well known examples e g the easi ness of omega are immediate consequences of this general theorem

solving biobjective combinatorial max ordering problems by ranking methods and a two phases approach abstract in this paper we propose a new method to solve biobjective combinatorial optimization problems of the max ordering type the method is based on the two phases method and ranking algorithms to efficiently construct k best solutions for the underlying single objective combinatorial problem we show that the method overcomes some of the difficulties of procedures proposed earlier we illustrate this by an example and discuss the difficulties in extending it to more than two objectives

solving some lexicographic multi objective combinatorial problems abstract the lexicographic multi objective optimization problem r lmop with r sum or bottleneck objectives optimizes a first objective then as far as a choice remains a second one then a third one and so on a general solution scheme from literature is based on scaling for the case that only sum criteria are involved the complexity is o rlogn t n m with t n m the complexity of optimization on combinatorial sum problem instances with m arcs and n nodes for cases with at least one bottleneck criterion the complexity is at least o rnlog2n t n m we describe a solution scheme that is suited to solve the shortest path r lmop the minimum spanning tree r lmop and the linear assignment r lmop the complexity is in all cases o r t n m

the completeness theorem for typing λ terms abstract rules for assigning type schemes to untyped terms are given three different semantics are described and the rules are proved complete with respect to two of these semantics the type schemes are built up from type variables not constants by the semantics are defined in arbitrary models of the untyped calculus such models do not come with a type structures as part of their definition the fact that two distinct semantics are completely captured by one set of rules says that the usual type language with as its only connective is not expressive enough to describe the differences between them i conjecture that the rules are also complete with respect to the third semantics

minimal counterexamples for linear time probabilistic verification abstract counterexamples for property violations have a number of important applications like supporting the debugging of erroneous systems and verifying large systems via counterexample guided abstraction refinement in this paper we propose the usage of minimal critical subsystems of discrete time markov chains and markov decision processes as counterexamples for violated regular properties minimality can thereby be defined in terms of the number of states or transitions this problem is known to be np complete for markov decision processes we show how to compute such subsystems using mixed integer linear programming and evaluate the practical applicability in a number of experiments they show that our method yields substantially smaller counterexample than using existing techniques

finding the k shortest paths we give algorithms for finding the k shortest paths not required to be simple connecting a pair of vertices in a digraph our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges in time o m n log n k we can also find the k shortest paths from a given source s to each vertex in the graph in total time o m n log n kn we describe applications to dynamic programming problems including the knapsack problem sequence alignment maximum inscribed polygons and genealogical relationship discovery

labeled random finite sets and the bayes multi target tracking filter an analytic solution to the multi target bayes recursion known as the delta generalized labeled multi bernoulli delta glmb filter has been recently proposed by vo and vo in labeled random finite sets and multi object conjugate priors ieee trans signal process vol 61 no 13 pp 3460 3475 2014 as a sequel to that paper the present paper details efficient implementations of the delta glmb multi target tracking filter each iteration of this filter involves an update operation and a prediction operation both of which result in weighted sums of multi target exponentials with intractably large number of terms to truncate these sums the ranked assignment and k th shortest path algorithms are used in the update and prediction respectively to determine the most significant terms without exhaustively computing all of the terms in addition using tools derived from the same framework such as probability hypothesis density filtering we present inexpensive relative to the delta glmb filter look ahead strategies to reduce the number of computations characterization of the l 1 error in the multi target density arising from the truncation is presented

three stage approaches for optimizing some variations of the resource constrained shortest path sub problem in a column generation context this paper presents a unified three stage approach tsa comprising preprocessing setup and iterative solution stages for solving several variations of the resource constrained shortest path problem rcsp tsa is designed specially for column generation applications in which sub problems must be solved repetitively the first two stages are implemented one time and only the third stage need be applied repetitively in a companion paper the authors proposed a tsa for solving rcsp on an acyclic graph with upper bound resource limitation constraints this paper shows that a tsa can be designed to solve each of several related problems shortest path with equality resource limitation constraints shortest path with resource windows resource constrained k shortest path and multiple resource multiple choice knapsack a numerical example demonstrates application of a tsa to design an international assembly system and its supply chain using branch and price with multiple choice knapsack sub problems computational results show that our tsa can solve this sub problem effectively in such a column generation environment

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

undirected single source shortest paths with positive integer weights in linear time the single source shortest paths problem sssp is one of the classic problems in algorithmic graph theory given a positively weighted graph g with a source vertex s find the shortest path from s to all other vertices in the graph since 1959 all theoretical developments in sssp for general directed and undirected graphs have been based on dijkstra s algorithm visiting the vertices in order of increasing distance from s thus any implementation of dijkstra s algorithm sorts the vertices according to their distances from s however we do not know how to sort in linear time here a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights the algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure identifying vertex pairs that may be visited in any order

f semantics for type assignment systems abstract yokouchi h f semantics for type assignment systems theoretical computer science 129 1994 39 77 this paper develops f semantics for type systems that assign types to untyped terms curry s system is complete for f semantics but a polymorphic type assignment system is not so we introduce two additional rules fi and fe and show that a polymorphic type assignment system becomes complete for f semantics if we add these two rules furthermore we apply the same method to a polymorphic type assignment system without the equality rule and obtain a similar completeness result we also show that an intersection type assignment system is complete for f models if we add two rules defined on the basis of fi and fe

algorithms for finding the weight constrained k longest paths in a tree and the length constrained k maximum sum segments of a sequence in this work we obtain the following new results given a tree t v e with a length function e r and a weight function w e r a positive integer k and an interval l u the weight constrainedklongest paths problem is to find the k longest paths among all paths in t with weights in the interval l u we show that the weight constrainedklongest paths problem has a lower bound w vlogv k in the algebraic computation tree model and give an o vlogv k time algorithm for it given a sequence a a 1 a 2 a n of numbers and an interval l u we define the sum and length of a segment a i j to be a i a i 1 a j and j i 1 respectively the length constrainedkmaximum sum segments problem is to find the k maximum sum segments among all segments of a with lengths in the interval l u we show that the length constrainedkmaximum sum segments problem can be solved in o n k time