state morphism algebras general approach we present a complete description of subdirectly irreducible state bl algebras as well as of subdirectly irreducible state morphism bl algebras in addition we present a general theory of state morphism algebras that is algebras of general type with state morphism which is a fixed idempotent endomorphism we define a diagonal state morphism algebra and we show that every subdirectly irreducible state morphism algebra can be embedded into a diagonal one we describe generators of the varieties of state morphism algebras in particular generators of state morphism bl algebras state morphism mtl algebras state morphism non associative bl algebras and state morphism pseudo mv algebras

on the complexity of some colorful problems parameterized by treewidth in this paper we study the complexity of several coloring problems on graphs parameterized by the treewidth of the graph 1 the list coloring problem takes as input a graph g together with an assignment to each vertex v of a set of colors c v the problem is to determine whether it is possible to choose a color for vertex v from the set of permitted colors c v for each vertex so that the obtained coloring of g is proper we show that this problem is w 1 hard parameterized by the treewidth of g the closely related precoloring extension problem is also shown to be w 1 hard parameterized by treewidth 2 an equitable coloring of a graph g is a proper coloring of the vertices where the numbers of vertices having any two distinct colors differs by at most one we show that the problem is hard for w 1 parameterized by the treewidth plus the number of colors we also show that a list based variation list equitable coloring is w 1 hard for forests parameterized by the number of colors on the lists 3 the list chromatic number g l g of a graph g is defined to be the smallest positive integer r such that for every assignment to the vertices v of g of a list l v of colors where each list has length at least r there is a choice of one color from each vertex list l v yielding a proper coloring of g we show that the problem of determining whether g l g

the monadic second order logic of graphs ix machines and their behaviours abstract we establish that every monadic second order property of the behaviour of a machine transition systems and tree automata are typical examples of machines is a monadic second order property of the machine itself in this way we clarify the distinction between dynamic properties of machines i e properties of their behaviours and their static properties i e properties of the graphs or relational structures representing them it is important for program verification that the dynamic properties that one wants to verify can be formulated statically in the simplest possible way as a corollary of our main result we also obtain that the monadic theory of an algebraic tree is decidable

parameterized and approximation complexity of partial vc dimension abstract we introduce the problem partial vc dimension that asks given a hypergraph h x e and integers k and l whether one can select a set c x of k vertices of h such that the set e c e e of distinct hyperedge intersections with c has size at least l the sets e c define equivalence classes over e partial vc dimension is a generalization of vc dimension which corresponds to the case l 2 k and of distinguishing transversal which corresponds to the case l e the latter is also known as test cover in the dual hypergraph we also introduce the associated fixed cardinality maximization problem max partial vc dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices we study the algorithmic complexity of partial vc dimension and max partial vc dimension both on general hypergraphs and on more restricted instances in particular neighborhood hypergraphs of graphs

lower bounds for the happy coloring problems in this paper we study the maximum happy vertices and the maximum happy edges problems mhv and mhe for short very recently the problems attracted a lot of attention and were studied in agrawal 17 aravind et al 16 choudhari and reddy 18 misra and reddy 17 main focus of our work is lower bounds on the computational complexity of these problems established lower bounds can be divided into the following groups np hardness of the above guarantee parameterization kernelization lower bounds answering questions of misra and reddy 17 exponential lower bounds under the set cover conjecture and the exponential time hypothesis and inapproximability results moreover we present an mathcal o ell k randomized algorithm for mhv and an mathcal o 2 k algorithm for mhe where ell is the number of colors used and k is the number of required happy vertices or edges these algorithms cannot be improved to subexponential taking proved lower bounds into account

the parameterised complexity of list problems on graphs of bounded treewidth we consider the parameterised complexity of several list problems on graphs with parameter treewidth or pathwidth in particular we show that list edge chromatic number and list total chromatic number are fixed parameter tractable parameterised by treewidth whereas list hamilton path is w1 hard even parameterised by pathwidth these results resolve two open questions of fellows fomin lokshtanov rosamond saurabh szeider and thomassen 2011

mean square values of hecke l series formed with r th order characters let l be a number field containing the r th roots of unity starting with the rankin selberg convolution of a metaplectic eisenstein series on the r fold cover of gl 2 with itself we construct a dirichlet series defined over l whose coefficients involve the r th order twists of a fixed hecke l function we then observe that a group of functional equations can be naturally associated with this construction combining this with the convexity theorem for holomorphic functions of several complex variables we show that this object as a function of two complex variables admits meromorphic continuation to 2 as an application we obtain asymptotic formulae for mean square values of the r th order twists of an arbitrary hecke l function defined over l

computations by fly automata beyond monadic second order logic parameterized algorithms based on automata infinite automata computing their transitions problems described in monadic second order logic counting and other problems not expressible in monadic second order logic the validity of a monadic second order ms expressible property can be checked in linear time on graphs of bounded tree width or clique width given with appropriate decompositions this result is proved by constructing from the ms sentence expressing the property and an integer that bounds the tree width or clique width of the input graph a finite automaton intended to run bottom up on the algebraic term representing a decomposition of the input graph as we cannot construct practically the transition tables of these automata because they are huge we use fly automata whose states and transitions are computed on the fly only when needed for a particular input furthermore we allow infinite sets of states and we equip automata with output functions thus they can check properties that are not ms expressible and compute values for example the number of p colorings of a graph we obtain xp and fpt graph algorithms parameterized by tree width or clique width we show how to construct easily such algorithms by combining predefined automata for basic functions and properties these combinations reflect the structure of the ms formula that specifies the property to check or the function to compute

existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

obtaining planarity by contracting few edges the planar contraction problem is to test whether a given graph can be made planar by using at most k edge contractions this problem is known to be np complete we show that it is fixed parameter tractable when parameterized by k

a polynomial algorithm for the k cut problem for fixed k the k cut problem is to find a partition of an edge weighted graph into k nonempty components such that the total edge weight between components is minimum this problem is np complete for an arbitrary k and its version involving fixing a vertex in each component is np hard even for k 3 we present a polynomial algorithm for k fixed that runs in onki 2 3k 2 4tn m steps where tn m is the running time required to find the minimum s t cut on a graph with n vertices and m edges

counting modulo quantifiers on finite structures we give a combinatorial method for proving elementary equivalence in first order logic fo with counting modulo n quantifiers dn inexpressibility results for fo dn with built in linear order are also considered for instance the class of linear orders of length divisible by n 1 cannot be expressed in fo dn using this result we prove that comparing cardinalities or connectivity of ordered graphs are not definable in fo dn we also show that the height of complete n ary trees cannot be expressed in fo dn with linear order interpreting the predicate y nx as a complete n ary tree we show that the predicate y px cannot be defined in fo dn with linear order whenever p has a prime factor that does not divide n this solves the problem raised by niwi ski and stolboushkin lics 93 we also discuss a connection between our results and the well known open problem in circuit complexity theory whether acc nc1

towards fixed parameter tractable algorithms for abstract argumentation abstract argumentation frameworks have received a lot of interest in recent years most computational problems in this area are intractable but several tractable fragments have been identified in particular dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree width however these tractability results which were obtained via courcelle s theorem do not directly lead to efficient algorithms the goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree width for defining larger tractable fragments as a by product we will sharpen some known complexity results

improved integrality gap upper bounds for traveling salesperson problems with distances one and two abstract we prove new integrality gap upper bounds for the traveling salesperson problem with distances one and two 1 2 tsp we obtain these bounds by investigating the structure of the support graph of optimal solutions to the subtour elimination linear programming relaxation with one additional cutting plane inequality for undirected 1 2 tsp our main results are as follows all instances have an integrality gap of at most 5 4 instances admitting half integral solutions have integrality gap at most 7 6 instances admitting subcubic solutions of cost at most the order of the instance have integrality gap at most 10 9 even without the cutting plane this bound is tight and holds in particular for basic solutions in the fractional 2 matching polytope with cost at most the order of the instance for directed 1 2 tsp instances we show an integrality gap upper bound of 3 2 for general instances and of 5 4 for instances admitting half integral solutions we prove these bounds by providing local search algorithms that in polynomial time find 2 matchings with few components in the support of the solution we show that the run times of our algorithms cannot be considerably improved under standard complexity theoretic assumptions we show that finding improved tsp solutions via local search is intractable for edge change parameterized by the size of the neighborhoods even for instances with distances one and two this strengthens a result of daniel marx

tight lower bounds for certain parameterized np hard problems based on the framework of parameterized complexity theory we derive tight lower bounds on the computational complexity for a number of well known np hard problems we start by proving a general result namely that the parameterized weighted satisfiability problem on depth t circuits cannot be solved in time n o k m o 1 where n is the circuit input length m is the circuit size and k is the parameter unless the t 1 st level w t 1 of the w hierarchy collapses to fpt by refining this technique we prove that a group of parameterized np hard problems including weighted sat hitting set set cover and feature set cannot be solved in time n o k m o 1 where n is the size of the universal set from which the k elements are to be selected and m is the instance size unless the first level w 1 of the w hierarchy collapses to fpt we also prove that another group of parameterized problems which includes weightedq sat for any fixed q 2 clique independent set and dominating set cannot be solved in time n o k unless all search problems in the syntactic class snp introduced by papadimitriou and yannakakis are solvable in subexponential time note that all these parameterized problems have trivial algorithms of running time either n km o 1 or o n k

parameterized and subexponential time complexity of satisfiability problems and applications we study the parameterized and the subexponential time complexity of the weighted and the unweighted satisfiability problems on bounded depth normalized boolean circuits we establish relations between the subexponential time complexity of the weighted and the unweighted satisfiability problems and use them to derive relations among the subexponential time complexity of several np hard problem we then study the role of certain natural structural parameters of the circuit in characterizing the parameterized and the subexponential time complexity of the circuit satisfiability problems under consideration we obtain threshold functions on some circuit structural parameters including the depth the number of gates the fan in and the maximum number of variable occurrences that lead to tight characterizations of the parameterized and the subexponential time complexity of the circuit satisfiability problems under consideration

an algebraic theory of graph reduction we show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules the method is constructive in the sense that we describe an algorithm which will produce from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth k a set of rewrite rules that reduces any member of the class to one of finitely many graphs in a number of steps bounded by the size of the graph this reduction system corresponds to an algorithm that runs in time linear in the size of the graph

size and treewidth bounds for conjunctive queries this article provides new worst case bounds for the size and treewith of the result q d of a conjunctive query q applied to a database d we derive bounds for the result size q d in terms of structural properties of q both in the absence and in the presence of keys and functional dependencies these bounds are based on a novel coloring of the query variables that associates a coloring number c q to each query q intuitively each color used represents some possible entropy of that variable using this coloring number we derive tight bounds for the size of q d in case i no functional dependencies or keys are specified and ii simple functional dependencies keys are given these results generalize recent size bounds for join queries obtained by atserias et al 2008 in the case of arbitrary compound functional dependencies we use tools from information theory to provide lower and upper bounds establishing a close connection between size bounds and a basic question in information theory our new coloring scheme also allows us to precisely characterize both in the absence of keys and with simple keys the treewidth preserving queries the queries for which the treewidth of the output relation is bounded by a function of the treewidth of the input database finally we give some results on the computational complexity of determining the size bounds and of deciding whether the treewidth is preserved

hitting minors on bounded treewidth graphs ii single exponential algorithms abstract for a finite collection of graphs f the f m deletion resp f tm deletion problem consists in given a graph g and an integer k decide whether there exists s v g with s k such that g s does not contain any of the graphs in f as a minor resp topological minor we are interested in the parameterized complexity of both problems when the parameter is the treewidth of g denoted by tw and specifically in the cases where f contains a single connected planar graph h we present algorithms running in time 2 o tw n o 1 called single exponential when h is either p 3 p 4 c 4 the paw the chair and the banner for both h m deletion and h tm deletion and when h k 1 i with i 1 for h tm deletion some of these algorithms use the rank based approach introduced by bodlaender et al 2015 7 this is the second of a series of articles on this topic and the results given here together with other ones allow us in particular to provide a tight dichotomy on the complexity of h m deletion in terms of h

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

complexity of conflict free colorings of graphs we consider conflict free colorings of graph neighborhoods each vertex of the graph must be assigned a color so that for each vertex v there is at least one color appearing exactly once in the neighborhood of v the goal is to minimize the number of used colors we consider both the case of closed neighborhoods when the neighborhood of a node includes the node itself and the case of open neighborhoods when a node does not belong to its neighborhood in this paper we study complexity aspects of the problem we show that the problem of conflict free coloring of closed neighborhoods is np complete moreover we give non approximability results for the conflict free coloring of open neighborhoods from a positive point of view both problems become tractable if parameterized by the vertex cover number or the neighborhood diversity number of the graph we present simple algorithms which improve on existing results

parameterized algorithms for conflict free colorings of graphs abstract in this paper we study the conflict free coloring of graphs induced by neighborhoods a coloring of a graph is conflict free if every vertex has a uniquely colored vertex in its neighborhood the conflict free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict free we consider both closed neighborhoods where the neighborhood of a vertex includes itself and open neighborhoods where a vertex does not include in its neighborhood we study the parameterized complexity of conflict free closed neighborhood coloring and conflict free open neighborhood coloring problems we show that both problems are fixed parameter tractable fpt when parameterized by the cluster vertex deletion number of the input graph this generalizes the result of gargano and rescigno theoretical computer science 2015 that conflict free coloring is fpt parameterized by the vertex cover number also we show that both problems admit an additive constant approximation algorithm when parameterized by the distance to threshold graphs we also study the complexity of the problem on special graph classes for split graphs we give a polynomial time algorithm for closed neighborhood conflict free coloring problem whereas we show that open neighborhood conflict free coloring is np complete for cographs we show that conflict free closed neighborhood coloring can be solved in polynomial time and conflict free open neighborhood coloring need at most three colors we show that interval graphs can be conflict free colored using at most four colors

filters of residuated lattices and triangle algebras an important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic is that of a filter filters can be used amongst others to define congruence relations specific kinds of filters include boolean filters and prime filters in this paper we define several different filters of residuated lattices and triangle algebras and examine their mutual dependencies and connections triangle algebras characterize interval valued residuated lattices

compatibility of unrooted phylogenetic trees is fpt a collection of t1 t2 tk of unrooted leaf labelled phylogenetic trees all with different leaf sets is said to be compatible if there exists a tree t such that each tree ti can be obtained from t by deleting leaves and contracting edges determining compatibility is np hard and the fastest algorithm to date has worst case complexity of around nk time n being the number of leaves here we present an o nf k algorithm proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable fpt with respect to the number k of trees

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

first moment of hecke l functions with quartic characters at the central point in this paper we study the first moment of central values of hecke l functions associated with quartic characters

the monadic second order logic of graphs xiv uniformly sparse graphs and edge set quantifications we consider the class usk of uniformly k sparse simple graphs i e the class of finite or countable simple graphs every finite subgraph of which has a number of edges bounded by k times the number of vertices we prove that for each k every monadic second order formula intended to express a graph property that uses variables denoting sets of edges can be effectively translated into a monadic second order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in usk this result extends to the class of uniformly k sparse simple hypergraphs of rank at most m for any k and m it follows that every subclass of usk consisting of finite graphs of bounded clique width has bounded tree width clique width is a graph complexity measure similar to tree width and relevant to the construction of polynomial algorithms for np complete problems on special classes of graphs

uniform and nonuniform recognizability deterministic and nondeterministic finite state recognizability over finite structures are introduced in an algebraic setting avoiding detailed computational conventions as needed in the definition of finite state acceptors for deterministic recognizability the classical approach is adopted using a uniform homomorphism from the input domain consisting of terms into a finite algebra for the nondeterministic case we refer to relational input structures and to an acceptance via relational homomorphisms which are applied nonuniformly since they depend on the input structures we show how this approach encompasses known models of nondeterministic automata over finite words trees pictures and graphs and present some elementary metaresults connecting uniform recognizability nonuniform recognizability and monadic second order logic

incremental list coloring of graphs parameterized by conservation incrementally k list coloring a graph means that a graph is given by adding vertices step by step and for each intermediate step we ask for a vertex coloring such that each vertex has one of the colors specified by its associated list containing some of in total k colors we introduce the conservative version of this problem by adding a further parameter c n specifying the maximum number of vertices to be recolored between two subsequent graphs differing by one vertex the conservation parameter c models the natural quest for a modest evolution of the coloring in the course of the incremental process instead of performing radical changes we show that even on bipartite graphs the problem is np hard for k 3 and w 1 hard for an unbounded number of colors when parameterized by c in contrast also on general graphs the problem becomes fixed parameter tractable with respect to the combined parameter k c we prove that the problem has an exponential size kernel with respect to k c and there is no polynomial size kernel unless np conp poly furthermore we investigate the parameterized complexity on various subclasses of perfect graphs we show fixed parameter tractability for the combined parameter treewidth and number k of colors finally we provide empirical findings on the practical relevance of our approach in terms of an effective graph coloring heuristic

the monadic second order logic of graphs x linear orderings graphs are finite and handled as relational structures we give some answers to the following general questions 1 1 for which classes of graphs c is it possible to specify a linear ordering of the set of vertices of each graph of c by fixed monadic second order formulas 2 2 for which classes of graphs c does there exist an extension l of monadic second order logic such that a subclass l of c is recognizable if and only if it is the class of graphs in c that satisfy a formula of l in this paper recognizability is understood in an algebraic sense relative to a finite set of graph operations and basic graphs that generate all graphs of c 3 3 for which classes of graphs c is it possible to construct in every graph of the class and by fixed formulas of a suitable extension of monadic second order logic its hierarchichal structure i e a finite term written with the operations and basic graphs of 2 that defines the considered graph applications concern dependency graphs of partially commutative words partial k paths cographs and graphs the modular decomposition of which uses prime graphs of bounded size

parameterized complexity of critical node cuts we consider the following graph cut problem called critical node cut cnc given a graph g on n vertices and two positive integers k and x determine whether g has a set of k vertices whose removal leaves g with at most x connected pairs of vertices we analyze this problem in the framework of parameterized complexity that is we are interested in whether or not this problem is solvable in f n o 1 time i e whether or not it is fixed parameter tractable for various natural parameters we consider four such parameters the size k of the required cut the upper bound x on the number of remaining connected pairs the lower bound y on the number of connected pairs to be removed the treewidth w of g we determine whether or not cnc is fixed parameter tractable for each of these parameters we determine this also for all possible aggregations of these four parameters apart from w k moreover we also determine whether or not cnc admits a polynomial kernel for all these parameterizations that is whether or not there is an algorithm that reduces each instance of cnc in polynomial time to an equivalent instance of size o 1 where is the given parameter

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

complexity of path forming games abstract for a number of two player games where players alternately choose the next vertex of a simple or an elementary path in a graph we consider the problem to determine whether for a given game instance there is a winning strategy for the first player we show several of these problems to be pspace complete in some special cases we obtain polynomial time algorithms based on graph rewriting or an intricate form of dynamic programming e g we show generalized geography and some other pspace complete problems to be linear time solvable on graphs with constant bounded treewidth

on the parameterized complexity of multiple interval graph problems multiple interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it many applications of interval graphs also generalize to multiple interval graphs often allowing for more robustness in the modeling of the specific application with this motivation in mind a recent systematic study of optimization problems in multiple interval graphs was initiated in this sequel we study multiple interval graph problems from the perspective of parameterized complexity the problems under consideration are k independent set k dominating set and k clique which are all known to be w 1 hard for general graphs and np complete for multiple interval graphs we prove that k clique is in fpt while k independent set and k dominating set are both w 1 hard we also prove that k independent dominating set a hybrid of the two above problems is also w 1 hard our hardness results hold even when each vertex is associated with at most two intervals and all intervals have unit length furthermore as an interesting byproduct of our hardness results we develop a useful technique for showing w 1 hardness via a reduction from the k multicolored clique problem a variant of k clique we believe this technique has interest in its own right as it should help in simplifying w 1 hardness results which are notoriously hard to construct and technically tedious

state operators on generalizations of fuzzy structures we enlarge the language of email protected monoids which are a non commutative generalizations of both mv algebras and bl algebras by adding a unary operation that describes algebraic properties of a state an analog of probability measures the resulting algebras are called email protected monoids and email protected monoids we present basic properties of such algebras we describe subdirectly irreducible algebras some generators of the varieties of state morphism email protected monoids and an interplay between states and state operators

intractability of clique width parameterizations we show that edge dominating set hamiltonian cycle and graph coloring are w 1 hard parameterized by clique width it was an open problem explicitly mentioned in several papers whether any of these problems is fixed parameter tractable when parameterized by the clique width that is solvable in time g k cdot n o 1 on n vertex graphs of clique width k where g is some function of k only our results imply that the running time o n f k of many clique width based algorithms is essentially the best we can hope for up to a widely believed assumption from parameterized complexity namely fpt neq w 1

data reductions fixed parameter tractability and random weighted d cnf satisfiability data reduction is a key technique in the study of fixed parameter algorithms in the ai literature pruning techniques based on simple and efficient to implement reduction rules also play a crucial role in the success of many industrial strength solvers understanding the effectiveness and the applicability of data reduction as a technique for designing heuristics for intractable problems has been one of the main motivations in studying the phase transition of randomly generated instances of np complete problems in this paper we take the initiative to study the power of data reductions in the context of random instances of a generic intractable parameterized problem the weighted d cnf satisfiability problem we propose a non trivial random model for the problem and study the probabilistic behavior of the random instances from the model we design an algorithm based on data reduction and other algorithmic techniques and prove that the algorithm solves the random instances with high probability and in fixed parameter polynomial time o d knm where n is the number of variables m is the number of clauses and k is the fixed parameter we establish the exact threshold of the phase transition of the solution probability and show that in some region of the problem space unsatisfiable random instances of the problem have parametric resolution proof of fixed parameter polynomial size also discussed is a more general random model and the generalization of the results to the model

the role of planarity in connectivity problems parameterized by treewidth for some years it was believed that for connectivity problems such as hamiltonian cycle algorithms running in time 2 o tw n o 1 called single exponential existed only on planar and other topologically constrained graph classes where tw stands for the treewidth of the n vertex input graph this was recently disproved by cygan et al 3 focs 2011 bodlaender et al 1 icalp 2013 and fomin et al 11 soda 2014 who provided single exponential algorithms on general graphs for most connectivity problems that were known to be solvable in single exponential time on topologically constrained graphs in this article we further investigate the role of planarity in connectivity problems parameterized by treewidth and convey that several problems can indeed be distinguished according to their behavior on planar graphs known results from the literature imply that there exist problems like cycle packing that cannot be solved in time 2 o tw log tw n o 1 on general graphs but that can be solved in time 2 o tw n o 1 when restricted to planar graphs our main contribution is to show that there exist natural problems that can be solved in time 2 o tw log tw n o 1 on general graphs but that cannot be solved in time 2 o tw log tw n o 1 even when restricted to planar graphs furthermore we prove that planar cycle packing and planar disjoint pathscannot be solved in time 2 o tw n o 1 the mentioned negative results hold unless the eth fails we feel that our results constitute a first step in a subject that can be further exploited

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

the monadic second order logic of graphs vii graphs as relational structures abstract relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied we define operations on structures that are compatible with monadic second order logic and that are powerful enough to represent context free graph and hypergraph grammars of various types namely the so called hyperedge replacement c ednce and separated handle rewriting grammars several results concerning monadic second order properties of the generated sets are obtained in a uniform way we also give a logical characterization of the equational sets of structures that generalizes the ones obtained by engelfriet and courcelle for hyperedge replacement and c ednce sets of graphs

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

local search is a ptas for feedback vertex set in minor free graphs abstract we show that an extremely simple local search gives a ptas for the feedback vertex set fvs problem in minor free graphs it keeps exchanging a constant number of vertices to improve the current solution until a local optimum is reached the previous ptas by fomin lokshtanov raman and saurabh 1 despite theoretical efficiency is much more complicated in the sense that it combines many advanced algorithmic tools such as contraction decomposition framework by demaine and hajiaghayi 2 courcelle s theorem 3 and the robertson and seymour decomposition 4 our main technical contribution is to show that the local optimum only differs the global optimum by a 1 factor we do so by introducing steiner points those who are not in the local and optimal solutions to the standard analysis of local search we believe that our technique is of independent interest

an initial study of time complexity in infinite domain constraint satisfaction abstract the constraint satisfaction problem csp is a widely studied problem with numerous applications in computer science and artificial intelligence for infinite domain csps there are many results separating tractable and np hard cases while upper and lower bounds on the time complexity of hard cases are virtually unexplored hence we initiate a study of the worst case time complexity of such csps we analyze backtracking algorithms and determine upper bounds on their time complexity we present asymptotically faster algorithms based on enumeration techniques and we show that these algorithms are applicable to well studied problems in for instance temporal reasoning finally we prove non trivial lower bounds applicable to many interesting csps under the assumption that certain complexity theoretic assumptions hold the gap between upper and lower bounds is in many cases surprisingly small which suggests that our upper bounds cannot be significantly improved

data reduction for graph coloring problems this paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances we are interested in how well polynomial time data reduction can provably shrink instances of coloring problems in terms of the chosen parameter it is well known that deciding 3 colorability is already np complete hence parameterizing by the requested number of colors is not fruitful instead we pick up on a research thread initiated by cai dam 2003 who studied coloring problems parameterized by the modification distance of the input graph to a graph class on which coloring is polynomial time solvable for example parameterizing by the number k of vertex deletions needed to make the graph chordal we obtain various upper and lower bounds for kernels of such parameterizations of q coloring complementing email protected s study of the time complexity with respect to these parameters our results show that the existence of polynomial kernels for q coloring parameterized by the vertex deletion distance to a graph class f is strongly related to the existence of a function f q which bounds the number of vertices which are needed to preserve the no answer to an instance of q list coloring on f

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

the monadic second order logic of graphs xii planar graphs and planar maps we prove that we can specify by formulas of monadic second order logic the unique planar embedding of a 3 connected planar graph if the planar graph is not 3 connected but given with a linear order of its set of edges we can also define a planar embedding by monadic second order formulas we cannot do so in general without the ordering even for 2 connected planar graphs the planar embedding of a graph can be specified by a relational structure called a map which is a graph enriched with a circular ordering of the edges incident with each vertex this circular ordering called a rotation system represents a planar embedding of the neighbourhood of each vertex for each connected map one can define a linear order on its vertices by formulas of monadic second order logic hence we have for planar graphs some kind of equivalence between linear orderings and planar embeddings

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

on residuated lattices with left and right internal state abstract in this paper notions of left and right state operators on residuated lattices are introduced and some related properties of such operators are investigated filters and normal filters generated by a subset in a state residuated lattice are characterized and it is shown that the lattice of filters forms a frame subdirectly irreducible state residuated lattices are characterized the notion of state coannihilator is introduced and a connection between them and galois connection is established finally it is shown that the set of state coannihilators forms a complete boolean algebra

constructing np intermediate problems by blowing holes with parameters of various properties the search for natural np intermediate problems is one of the holy grails within computational complexity ladner s original diagonalization technique for generating np intermediate problems blowing holes has a serious shortcoming it creates problems with a highly artificial structure by arbitrarily removing certain problem instances in this article we limit this problem by generalizing ladner s method to use parameters with various characteristics this allows one to define more fine grained parameters resulting in np intermediate problems where we only blow holes in a controlled subset of the problem we begin by fully characterizing the problems that admit np intermediate subproblems for a broad and natural class of parameterizations and extend the result further such that structural csp restrictions based on parameters that are hard to compute such as tree width are covered thereby generalizing a result by grohe for studying certain classes of problems including csps parameterized by constraint languages we consider more powerful parameterizations first we identify a new method for obtaining constraint languages such that csp are np intermediate the sets can have very different properties compared to previous constructions by for instance bodirsky grohe and provides insights into the algebraic approach for studying the complexity of infinite domain csps second we prove that the propositional abduction problem parameterized by constraint languages admits np intermediate problems this settles an open question posed by nordh zanuttini we provide a framework to obtain np intermediate problems based on diagonalization we categorize different types of parameters that are usable in our framework we construct np intermediate constraint satisfaction problems we resolve the open question whether boolean abduction admits intermediate problems

on parameterized exponential time complexity in this paper we study the notion of parameterized exponential time complexity we show that a parameterized problem can be solved in parameterized 2 o f k p n time if and only if it is solvable in time o 2 d f k q n for any constant d 0 where p and q are polynomials we then illustrate how this equivalence can be used to show that special instances of parameterized np hard problems are as difficult as the general instances for example we show that the planar dominating set problem on degree 3 graphs can be solved in 2 o k p n parameterized time if and only if the general planar dominating set problem can apart from their complexity theoretic implications our results have some interesting algorithmic implications as well

equitable colorings of bounded treewidth graphs a proper coloring of a graph g is equitable if the sizes of any two color classes differ by at most one a proper coloring is l bounded when each color class has size at most l we consider the problems to determine for a given graph g and a given integer l whether g has an equitable l bounded k coloring we prove that both problems can be solved in polynomial time on graphs of bounded treewidth and show that a precolored version remains np complete on trees

the distribution of general gauss sums and similar arithmetic functions at prime arguments on axiomatise les arguments donnes par heath brown et patterson 1979 jusqu a une extension donnee afin de les rendre applicables a des fonctions arithmetiques autres que les sommes de gauss

double dirichlet series and the n th order twists of hecke l series let n 3 be a fixed integer and let f be a global field containing the n th roots of unity in this paper we study the collective behavior of the n th order twists of a fixed hecke l series for f to do so we introduce a double dirichlet series in two complex variables s w which is a weighted sum of the twists and obtain its meromorphic continuation we also study related sums of n th order gauss sums these objects together satisfy a nonabelian group of functional equations in s w of order 32

on the parameterized complexity of recognizing well covered r l graph an r ell partition of a graph g is a partition of its vertex set into r independent sets and ell cliques a graph is r ell if it admits an r ell partition a graph is well covered if every maximal independent set is also maximum a graph is r ell well covered if it is both r ell and well covered in this paper we consider two different decision problems in the r ell well covered graph problem r ell wcg for short we are given a graph g and the question is whether g is an r ell well covered graph in the well covered r ell graph problem wc r ell g for short we are given an r ell graph g together with an r ell partition of v g into r independent sets and ell cliques and the question is whether g is well covered we classify most of these problems into p conp complete np complete np hard or conp hard only the cases wc r 0 g for r ge 3 remain open in addition we consider the parameterized complexity of these problems for several choices of parameters such as the size alpha of a maximum independent set of the input graph its neighborhood diversity or the number ell of cliques in an r ell partition in particular we show that the parameterized problem of deciding whether a general graph is well covered parameterized by alpha can be reduced to the wc 0 ell g problem parameterized by ell and we prove that this latter problem is in xp but does not admit polynomial kernels unless mathsf conp subseteq mathsf np mathsf poly

half integrality lp branching and fpt algorithms a recent trend in parameterized algorithms is the application of polytope tools to fixed parameter tractable fpt algorithms e g cygan et al focs 2011 52nd annual symposium on foundations of computer science ieee 2011 pp 150 159 narayanaswamy et al stacs 2012 symposium on theoretical aspects of computer science 2012 pp 338 349 although this approach has yielded significant speedups for a range of important problems it requires the underlying polytope to have very restrictive properties including half integrality and nemhauser trotter style persistence properties to date these properties are essentially known to hold only for two classes of polytopes covering the cases of vertex cover nemhauser and trotter math program 8 1975 pp 232 248 and node multiway cut garg et al j alg 50 2004 pp 49 61 taking a slightly different approach we view half integrality as a discrete relaxation of a problem e g a relaxation of the search space from 0 1 v to 0

tight complexity bounds for fpt subgraph problems parameterized by the clique width we give tight algorithmic lower and upper bounds for some double parameterized subgraph problems when the clique width of the input graph is one of the parameters

on the compressibility of mathcal np instances and cryptographic applications we study compression that preserves the solution to an instance of a problem rather than preserving the instance itself our focus is on the compressibility of mathcal np decision problems we consider mathcal np problems that have long instances but relatively short witnesses the question is whether one can efficiently compress an instance and store a shorter representation that maintains the information of whether the original input is in the language or not we want the length of the compressed instance to be polynomial in the length of the witness and polylog in the length of original input such compression enables succinctly storing instances until a future setting will allow solving them either via a technological or algorithmic breakthrough or simply until enough time has elapsed in this paper we first develop the basic complexity theory of compression including reducibility completeness and a stratification of mathcal np with respect to compression we then show that compressibility say of sat would have vast implications for cryptography including constructions of one way functions and collision resistant hash functions from any hard on average problem in mathcal np and cryptanalysis of key agreement protocols in the bounded storage model when mixed with time complexity based cryptography