### Quantum Query Complexity of Multilinear Identity Testing

Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an additive generating set and a multilinear polynomial over that ring, also accessed as a black-box function (we allow the indeterminates of the polynomial to be commuting or noncommuting), we study the problem of testing if the polynomial is an \emph{identity} for the given ring. We give a quantum...

### Harnessing the Multicores: Nested Data Parallelism in Haskell

Simon Peyton Jones, Roman Leshchinskiy, Gabriele Keller & Manuel M T Chakravarty
If you want to program a parallel computer, a purely functional language like Haskell is a promising starting point. Since the language is pure, it is by-default safe for parallel evaluation, whereas imperative languages are by-default unsafe. But that doesn\'t make it easy! Indeed it has proved quite difficult to get robust, scalable performance increases through parallel functional programming, especially as the number of processors increases. A particularly promising and well-studied approach to employing large...

### 2008 Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

Ramesh Hariharan, Madhavan Mukund & V Vinay
This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS). This year's conference attracted 117 submissions. Each submission was reviewed by at least three independent referees. The final selection of the papers making up the programme was done through an electronic discussion on EasyChair, spanning two weeks, without a...

### Analyzing the Implicit Computational Complexity of object-oriented programs

Jean-Yves Marion & Romain Pechoux
A sup-interpretation is a tool which provides upper bounds on the size of the values computed by the function symbols of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. This paper is an attempt to adapt the framework of sup-interpretations to a fragment of object-oriented programs, including loop and while constructs and methods with side effects. We give a criterion, called brotherly criterion, which uses the...

### A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems

Juan Rodriguez-Hortala
Formalisms involving some degree of nondeterminism are frequent in computer science. In particular, various programming or specification languages are based on term rewriting systems where confluence is not required. In this paper we examine three concrete possible semantics for non-determinism that can be assigned to those programs. Two of them --call-time choice and run-time choice-- are quite well-known, while the third one --plural semantics-- is investigated for the first time in the context of term...

### Banach-Mazur Games on Graphs

Erich Graedel
We survey determinacy, definability, and complexity issues of Banach-Mazur games on finite and infinite graphs. Infinite games where two players take turns to move a token through a directed graph, thus tracing out an infinite path, have numerous applications in different branches of mathematics and computer science. In the usual format, the possible moves of the players are given by the edges of the graph; in each move a player takes the token from its...

### Average-Time Games

Marcin Jurdzinski & Ashutosh Trivedi
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimize the average time per transition and player Max wants to maximize it. A solution of average-time games is presented using a reduction to average-price game on a finite graph. A direct consequence is...

### On Estimation Algorithms vs Approximation Algorithms

Uriel Feige
In a combinatorial optimization problem, when given an input instance, one seeks a feasible solution that optimizes the value of the objective function. Many combinatorial optimization problems are NP-hard. A way of coping with NP-hardness is by considering approximation algorithms. These algorithms run in polynomial time, and their performance is measured by their approximation ratio: the worst case ratio between the value of the solution produced and the value of the (unknown) optimal solution. In...

### Leaf languages and string compression

Markus Lohrey
Tight connections between leafs languages and strings compressed via straight-line programs (SLPs) are established. It is shown that the compressed membership problem for a language $L$ is complete for the leaf language class defined by $L$ via logspace machines. A more difficult variant of the compressed membership problem for $L$ is shown to be complete for the leaf language class defined by $L$ via polynomial time machines. As a corollary, a fixed linear visibly pushdown...

### A Cubic-Vertex Kernel for Flip Consensus Tree

Christian Komusiewicz & Johannes Uhlmann
Given a bipartite graph G=(V_c,V_t,E) and a non-negative integer k, the NP-complete Minimum-Flip Consensus Tree problem asks whether G can be transformed, using up to k edge insertions and deletions, into a graph that does not contain an induced P_5 with its first vertex in V_t (a so-called M-graph or Sigma-graph). This problem plays an important role in computational phylogenetics, V_c standing for the characters and V_t standing for taxa. Chen et al. [IEEE/ACM TCBB...

### Dynamic matrix rank with partial lookahead

Telikepalli Kavitha
We consider the problem of maintaining information about the rank of a matrix $M$ under changes to its entries. For an $n \times n$ matrix $M$, we show an amortized upper bound of $O(n^{\omega-1})$ arithmetic operations per change for this problem, where $\omega < 2.376$ is the exponent for matrix multiplication, under the assumption that there is a {\em lookahead} of up to $\Theta(n)$ locations. That is, we know up to the next $\Theta(n)$ locations...

### STCON in Directed Unique-Path Graphs

Sampath Kannan, Sanjeev Khanna & Sudeepa Roy
We study the problem of space-efficient polynomial-time algorithms for {\em directed st-connectivity} (STCON). Given a directed graph $G$, and a pair of vertices $s, t$, the STCON problem is to decide if there exists a path from $s$ to $t$ in $G$. For general graphs, the best polynomial-time algorithm for STCON uses space that is only slightly sublinear. However, for special classes of directed graphs, polynomial-time poly-logarithmic-space algorithms are known for STCON. In this paper,...

### An Optimal Construction of Finite Automata from Regular Expressions

Stefan Gulan & Henning Fernau
We consider the construction of finite automata from their corresponding regular expressions by a series of digraph-transformations along the expression\'s structure. Each intermediate graph represents an extended finite automaton accepting the same language. The character of our construction allows a fine-grained analysis of the emerging automaton\'s size, eventually leading to an optimality result.

### The Complexity of Tree Transducer Output Languages

Kazuhiro Inaba & Sebastian Maneth
Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in $\NSPACE(n)$ and hence are context-sensitive, and the class is NP-complete.

### The unfolding of general Petri nets

Jonathan Hayman & Glynn Winskel
The unfolding of (1-)safe Petri nets to occurrence nets is well understood. There is a universal characterization of the unfolding of a safe net which is part and parcel of a coreflection from the category of occurrence nets to the category of safe nets. The unfolding of general Petri nets, nets with multiplicities on arcs whose markings are multisets of places, does not possess a directly analogous universal characterization, essentially because there is an implicit...

### Explicit Muller Games are PTIME

Florian Horn
Regular games provide a very useful model for the synthesis of controllers in reactive systems. The complexity of these games depends on the representation of the winning condition: if it is represented through a win-set, a coloured condition, a Zielonka-DAG or Emerson-Lei formulae, the winner problem is \pspace-complete; if the winning condition is represented as a Zielonka tree, the winner problem belongs to \np and \conp. In this paper, we show that explicit Muller games...

### Abstraction Refinement for Games with Incomplete Information

Rayna Dimitrova & Bernd Finkbeiner
Counterexample-guided abstraction refinement (CEGAR) is used in automated software analysis to find suitable finite-state abstractions of infinite-state systems. In this paper, we extend CEGAR to games with incomplete information, as they commonly occur in controller synthesis and modular verification. The challenge is that, under incomplete information, one must carefully account for the knowledge available to the player: the strategy must not depend on information the player cannot see. We propose an abstraction mechanism for games...

### A new approach to the planted clique problem

Alan Frieze & Ravi Kannan
We study the problem of finding a large planted clique in the random graph $G_{n,1/2}$. We reduce the problem to that of maximising a three dimensional tensor over the unit ball in $n$ dimensions. This latter problem has not been well studied and so we hope that this reduction will eventually lead to an improved solution to the planted clique problem.

### All-Norms and All-L_p-Norms Approximation Algorithms

Daniel Golovin, Anupam Gupta, Amit Kumar & Kanat Tangwongsan
In many optimization problems, a solution can be viewed as ascribing a cost\'\' to each client, and the goal is to optimize some aggregation of the per-client costs. We often optimize some $L_p$-norm (or some other symmetric convex function or norm) of the vector of costs---though different applications may suggest different norms to use. Ideally, we could obtain a solution that optimizes several norms simultaneously. In this paper, we examine approximation algorithms that simultaneously perform...

### 3-connected Planar Graph Isomorphism is in Log-space

Samir Datta, Nutan Limaye & Prajakta Nimbhorkar
We consider the isomorphism and canonization problem for $3$-connected planar graphs. The problem was known to be \Log-hard and in \ULcoUL\ \cite{TW07}. In this paper, we give a deterministic log-space algorithm for $3$-connected planar graph isomorphism and canonization. This gives an \Log-completeness result, thereby settling its complexity. \par The algorithm uses the notion of universal exploration sequences from \cite{koucky01} and \cite{Rei05}. To our knowledge, this is a completely new approach to graph canonization.

### A new upper bound for 3-SAT

Josep Diaz, Lefteris Kirousis, Dieter Mitsche & Xavier Perez-Gimenez
We show that a randomly chosen $3$-CNF formula over $n$ variables with clauses-to-variables ratio at least $4.4898$ is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was $4.506$. The first such bound, independently discovered by many groups of researchers since 1983, was $5.19$. Several decreasing values between $5.19$ and $4.506$ were published in the years between. The probabilistic techniques we use for the proof are, we believe, of independent...

### Graph Games on Ordinals

Julien Cristau & Florian Horn
We consider an extension of Church\'s synthesis problem to ordinals by adding limit transitions to graph games. We consider game arenas where these limit transitions are defined using the sets of cofinal states. In a previous paper, we have shown that such games of ordinal length are determined and that the winner problem is \pspace-complete, for a subclass of arenas where the length of plays is always smaller than $\omega^\omega$. However, the proof uses a...

### Pruning 2-Connected Graphs

Chandra Chekuri & Nitish Korula
Given an edge-weighted undirected graph $G$ with a specified set of terminals, let the \emph{density} of any subgraph be the ratio of its weight/cost to the number of terminals it contains. If $G$ is 2-connected, does it contain smaller 2-connected subgraphs of density comparable to that of $G$? We answer this question in the affirmative by giving an algorithm to \emph{prune} $G$ and find such subgraphs of any desired size, at the cost of only...

### Single-Sink Network Design with Vertex Connectivity Requirements

Chandra Chekuri & Nitish Korula
We study single-sink network design problems in undirected graphs with vertex connectivity requirements. The input to these problems is an edge-weighted undirected graph $G=(V,E)$, a sink/root vertex $r$, a set of terminals $T \subseteq V$, and integer $k$. The goal is to connect each terminal $t \in T$ to $r$ via $k$ \emph{vertex-disjoint} paths. In the {\em connectivity} problem, the objective is to find a min-cost subgraph of $G$ that contains the desired paths. There...

### On the Power of Imperfect Information

Dietmar Berwanger & Laurent Doyen
We present a polynomial-time reduction from parity games with imperfect information to safety games with imperfect information. Similar reductions for games with perfect information typically increase the game size exponentially. Our construction avoids such a blow-up by using imperfect information to realise succinct counters which cover a range exponentially larger than their size. In particular, the reduction shows that the problem of solving imperfect-information games with safety conditions is \EXPTIME-complete.

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