Showing papers in "International Journal of Foundations of Computer Science in 2014"

Asynchronous signal passing for tile self-assembly: fuel efficient computation and efficient assembly of shapes

Abstract: In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.

Active tile self-assembly, part 1: universality at temperature 1

Abstract: We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. We also prove that this model has universal computational power in 2D at temperature 1 by showing an active tile assembly construction that simulates one-dimensional cellular automata in 2D at temperature 1.

Zoom structures and reaction systems yield exploration systems

Abstract: In this paper we extend the framework of reaction systems by introducing (extended) zoom structures which formalize a depository of knowledge of a discipline of science. The integrating structure of such a depository (which is a well-founded partial order) allows one to deal with the hierarchical nature of biology. This leads to the notion of an exploration system which consists of (1) a static part which is a depository of knowledge given by an extended zoom structure , and (2) a dynamic part given by a family of reaction systems . In this setup the depository of knowledge is explored by computations/processes provided by reaction systems from , where this exploration can use/integrate knowledge present on different levels (e.g., atomic, cellular, organism, species, … levels).

Active tile self-assembly, part 2: self-similar structures and structural recursion

Abstract: We introduce a mathematical framework to describe self-similarity and structural recursion within the active tile self-assembly model, thereby providing a connection between substitution tiling and algorithmic self-assembly. We show that one such structurally recursive assembly system can simulate the dynamics of the self-similar substitution tiling known as the L-shape tiling.

Limited automata and regular languages

Abstract: Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1-limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1-limited automata and one-way deterministic finite automata. The gap reduces to a single exponential in the case of deterministic 1-limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1-limited automata. Another consequence is that 1-limited automata can have less states than equivalent two-way nondeterministic finite automata. We show that this is true even if we restrict to the case of the one-letter input alphabet. For each d ≥ 2, d-limited automata are known to characterize the class of context-free languages. Using the Chomsky-Schutzenberger representation for contextfree languages, we present a new conversion from context-free languages into 2-limited automata.

Online scheduling of mixed cpu-gpu jobs

Abstract: We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

Prefix picture codes: a decidable class of two-dimensional codes.

Abstract: A two-dimensional code of pictures is defined as a set X ⊆ Σ** such that any picture over Σ is tilable in at most one way with pictures in X. It is proved that in general it is undecidable whether a finite set of picture is a code. The subclass of prefix codes is introduced and it is proved that it is decidable whether a finite set of pictures is a prefix code. Further a polynomial time decoding algorithm for finite prefix codes is given. Maximality and completeness of finite prefix codes are studied.

Applications of finsler geometry to speed limits to quantum information processing

Abstract: We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Here, we discuss speed limits in the context of quantum computing. We review some relevant parts of the theory of Finsler metrics on Lie groups and homogeneous spaces such as the special unitary groups and complex projective spaces. We show how these constructions can be applied to analysing the limit to the speed of quantum information processing operations in constrained quantum systems with finite dimensional Hilbert spaces of states. We demonstrate the approach applied to a spin chain system.

ON SCHEDULING SERIES-PARALLEL DAGs TO MAXIMIZE AREA

Abstract: The AREA of a schedule for executing DAGs is the average number of DAG-chores that are eligible for execution at each step of the computation. AREA maximization is a new optimization goal for sched...

Simple reaction systems and their classification

Abstract: Reaction systems are a model of computation inspired by biochemical reactions involving reactants, inhibitors and products from a finite background set. We define a notion of multi-step simulation among reaction systems and derive a classification with respect to the amount of resources (reactants and inhibitors) involved in each reaction. We prove that “simple” reaction systems, having at most one reactant and one inhibitor per reaction, suffice in order to simulate arbitrary systems. Finally, we show that the equivalence relation of mutual simulation induces exactly five linearly ordered classes of reaction systems characterizing well-known subclasses of the functions over Boolean lattices, such as the constant, additive (join-semilattice endomorphisms), monotone, and antitone functions.

Tractable and intractable variations of unordered tree edit distance

Abstract: In this paper, we investigate the problem of computing structural sensitive variations of an unordered tree edit distance. First, we focus on the variations tractable by the algorithms including the submodule of a network algorithm, either the minimum cost maximum flow algorithm or the maximum weighted bipartite matching algorithm. Then, we show that both network algorithms are replaceable, and hence the time complexity of computing these variations can be reduced to O(nmd) time, where n is the number of nodes in a tree, m is the number of nodes in another tree and d is the minimum degree of given two trees. Next, we show that the problem of computing the bottom-up distance is MAX SNP-hard. Note that the well-known linear-time algorithm for the bottom-up distance designed by Valiente (2001) computes just a bottom-up indel (insertion-deletion) distance allowing no substitutions.

Sorting conjugates and suffixes of words in a multiset

Abstract: In this paper we are interested in the study of the combinatorial aspects related to the extension of the Burrows-Wheeler transform to a multiset of words. Such study involves the notion of suffixes and conjugates of words and is based on two different order relations, denoted by

The chomsky-schützenberger theorem for quantitative context-free languages

Abstract: Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative context-free languages assume only finitely many values.

An analogue-digital Church-Turing Thesis

Abstract: We argue that dynamical systems involving discrete and continuous data can be modelled by Turing machines with oracles that are physical processes. Using the theory introduced in Beggs et al. [2,3], we consider the scope and limits of polynomial time computations by such systems. We propose a general polynomial time Church-Turing Thesis for feasible computations by analogue-digital systems, having the non-uniform complexity class BPP//log* as theoretical upper bound. We show why BPP//log* should be replace P/poly, which was proposed by Siegelmann for neural nets [23,24]. Then we examine whether other sources of hypercomputation can be found in analogue-digital systems besides the oracle itself. We prove that the higher polytime limit P/poly can be attained via non-computable analogue-digital interface protocols.

A class of 1-resilient boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks

Abstract: Recently, Tang, Carlet and Tang presented a combinatorial conjecture about binary strings, allowing proving that all balanced functions in some infinite class they introduced have optimal algebraic immunity. Later, Cohen and Flori completely proved that the conjecture is true. These functions have good (provable or at least observable) cryptographic properties but they are not 1-resilient, which represents a drawback for their use as filter functions in stream ciphers. We propose a construction of an infinite class of 1-resilient Boolean functions with optimal algebraic immunity by modifying the functions in this class. The constructed functions have optimal algebraic degree, that is, meet the Siegenthaler bound, and high nonlinearity. We prove a lower bound on their nonlinearity, but as for the Carlet-Feng functions and for the functions mentioned above, this bound is not enough for ensuring a nonlinearity sufficient for allowing resistance to the fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for small numbers of variables. Our computations show that the functions in this class have very good nonlinearity and also good immunity to fast algebraic attacks. This is the first time that an infinite class of functions gathers all of the main criteria allowing these functions to be used as filters in stream ciphers.

Adjacent Ordered Multi-Pushdown Systems

Abstract: Multi-pushdown systems are formal models of multi-threaded programs. As they are Turing powerful in their full generality, several decidable subclasses, constituting under-approximations of the original system, have been studied in the recent years. Ordered Multi-Pushdown Systems (OMPDSs) impose an order on the stacks and limit pop actions to the lowest non-empty stack. The control state reachability for OMPDSs is 2-ETIME-COMPLETE. We propose a restriction on OMPDSs, called Adjacent OMPDSs (AOMPDS), where values may be pushed only on the lowest non-empty stack or one of its two neighbours. We describe EXPTIME decision procedures for reachability and LTL model-checking and establish matching lower bounds. We demonstrate the utility of this model as an algorithmic tool via optimal reductions from other models.

Yao's millionaires' problem and decoy-based public key encryption by classical physics

Abstract: We use various laws of classical physics to offer several solutions of Yao's millionaires' problem without using any one-way functions. We also describe several informationally secure public key encryption protocols, i.e., protocols secure against passive computationally unbounded adversary. This introduces a new paradigm of decoy-based cryptography, as opposed to “traditional” complexity-based cryptography. In particular, our protocols do not employ any one-way functions.

Online minimum makespan scheduling with a buffer

Abstract: In this paper we study an online minimum makespan scheduling problem with a reordering buffer. We obtain the following results: (i) for m > 51 identical machines, we give a 1.5-competitive online algorithm with a buffer of size ⌈1.5m⌉; (ii) for three identical machines, we give an optimal online algorithm with a buffer size six, better than the previous nine; (iii) for m uniform machines, using a buffer of size m, we improve the competitive ratio from 2 + e to 2 − 1/m+ e, where e > 0 is sufficiently small and m is a constant.

Nondeterministic biautomata and their descriptional complexity

Abstract: We investigate the descriptional complexity of nondeterministic biautomata, which are a generalization of biautomata [O. KLIMA, L. POLAK: On biautomata. RAIRO — Theor. Inf. Appl., 46(4), 2012]. Simply speaking, biautomata are finite automata reading the input from both sides; although the head movement is nondeterministic, additional requirements enforce biautomata to work deterministically. First we study the size blow-up when determinizing nondeterministic biautomata. Further, we give tight bounds on the number of states for nondeterministic biautomata accepting regular languages relative to the size of ordinary finite automata, regular expressions, and syntactic monoids. It turns out that as in the case of ordinary finite automata nondeterministic biautomata are superior to biautomata with respect to their relative succinctness in representing regular languages.

Zero-knowledge blackbox testing: where are the faults?

Abstract: We derive a quantitative relationship between the maximal entropy rate achieved by a blackbox software system's specification graph, and the probability of faults Pn obtained by testing the system, as a function of the length n of a test sequence. By equating “blackbox” to the maximal entropy principle, we model the specification graph as a Markov chain that, for each distinct value of n, achieves the maximal entropy rate for that n. Hence the Markov transition probability matrices are not constant in n, but form a sequence of transition matrices T1,…, Tn. We prove that, for nontrivial specification graphs, the probability of finding faults goes asymptotically to zero as the test length n increases, regardless of the evolution of Tn. This implies that zero-knowledge testing is practical only for small n. We illustrate the result using a concrete example of a system specification graph for an autopilot control system, and plot its curve Pn.

The ranges of state complexities for complement, star, and reversal of regular languages

Abstract: We examine the deterministic and nondeterministic state complexity of complements, stars, and reversals of regular languages. Our results are as follows: (1) The nondeterministic state complexity of the complement of an n-state nfa language over a five-letter alphabet may reach each value from log n to 2n. (2) The state complexity of the star (reversal) of an n-state dfa language over a growing alphabet may reach each value from 1 to (from log n to 2n, respectively). (3) The nondeterministic state complexity of the star (reversal) of an n-state nfa binary language may reach each value from 1 to n + 1 (from n - 1 to n + 1, respectively). We also obtain some partial results on the nondeterministic state complexity of complements of binary regular languages. As a bonus, we get an exponential number of values that are non-magic in the binary case.

On the number of abelian bordered words (with an example of automatic theorem-proving)

Abstract: In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in ℤ not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a 3-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we characterize the lengths of the abelian unbordered factors occurring in the Thue–Morse word using some kind of automatic theorem-proving provided by a logical characterization of the k-automatic sequences.

Finite automata with advice tapes

Abstract: We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.

Towards computation with microchemomechanical systems

Abstract: Labs-on-chips are promising candidates for the realization of chemical information systems, where data are embodied in the form of chemical concentrations. In this paper we present the concept of microchemomechanical systems, a lab-on-a-chip technology based on intrinsically active components. The active components are valves fabricated from phase-changeable polymers that provide a direct feedback mechanism and exhibit a transistor-like functionality. Therefore this microfluidic platform facilitates the realization of logic operations, if-then structures and the sampling of chemical signals. In analogy with electronic von Neumann CPUs, control and execution unit are integrated on a single chip. Due to the intrinsic activity of the valves and their small size, microchemomechanical systems are highly suitable for large-scale integration.

Efficient grid exploration with a stationary token

Abstract: A mobile agent starting at an arbitrary node of an m × k grid, for 1 < m ≤ k, has to explore the grid by visiting all its nodes and traversing all edges. The cost of an exploration algorithm is the number of edge traversals by the agent. Nodes of the grid are unlabeled and ports at each node v have distinct numbers in {0,…, d − 1}, where d = 2, 3, 4 is the degree of v. Port numbering is local, i.e., there is no relation between port numbers at different nodes. When visiting a node the agent sees its degree. It also sees the port number by which it enters a node and can choose the port number by which it leaves a visited node. We are interested in deterministic exploration algorithms working at low cost. We consider the scenario in which the agent is equipped with a stationary token situated at its starting node. The agent sees the token whenever it visits this node. We give an exploration algorithm working at cost O(k2) for 2 × k grids, and at cost O(m2k), for m × k grids, when 2 < m ≤ k.

New worst-case upper bound for counting exact satisfiability

Abstract: The counting exact satisfiablity problem (#XSAT) is a problem that computes the number of truth assignments satisfying only one literal in each clause. This paper presents an algorithm that solves the #XSAT problem in O(1.1995n), which is faster than the best algorithm running in O(1.2190n), where n denotes the number of variables. To increase the efficiency of the algorithm, a new principle, called common literals principle, is addressed to simplify formulae. This allows us to further eliminate literals. In addition, we firstly apply the resolution principles into solving #XSAT problem, and therefore it improves the efficiency of the algorithm further.

CONSTRUCTING 2m-VARIABLE BOOLEAN FUNCTIONSWITH OPTIMAL ALGEBRAIC IMMUNITY BASED ON POLAR DECOMPOSITION OF $\mathbb{F}^\ast_{2^{2m}}$

Abstract: Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field $\mathbb{F}^\ast_{2^{2m}}$ seems to be a promising approach s...

P automata with restricted power

Abstract: P automata are variants of symport/antiport membrane systems which describe string languages by applying a mapping to the sequence of multisets entering the system during computations. In this paper, we study their computational power in the case when the input mapping associates each input multiset with the set of strings consisting of all permutations of its elements. We show that P automata of this type are strictly less powerful than so-called restricted logarithmic space Turing machines, and we also exhibit a strict infinite hierarchy within the accepted language class based on the number of membranes present in the system.

Super edge connectivity of kronecker products of graphs

Abstract: A graph G is said to be super edge connected (in short super – λ) if every minimum edge cut isolates a vertex of G. The Kronecker product of graphs G and H is the graph with vertex set V(G × H) = V(G) × V(H), where two vertices (u1, v1) and (u2, v2) are adjacent in G × H if u1u2 ∈ E(G) and v1v2 ∈ E(H). Let G be a connected graph, and let δ(G) and λ(G) be the minimum degree and the edge-connectivity of G, respectively. In this paper we prove that G × Kn is super-λ for n ≥ 3, if λ(G) = δ(G) and G ≇ K2. Furthermore, we show that K2 × Kn is super-λ when n ≥ 4. Similar results for G × Tn are also obtained, where Tn is the graph obtained from Kn by adding a loop to every vertex of Kn.

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

Abstract: The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. In the preliminary version of this paper, we built the probabilistic safety vector (PSV) with modified cycle patterns and developed the routing algorithm to decide the fault-free routing path with the help of PSV. Afterwards, we observed that the routing performance of PSV gets worse as the percentage of fault nodes increases, especially it exceeds 25%. In order to improve the routing performance with more faulty nodes, an adaptive method of threshold assignment for the PSV is also proposed. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, PSV with dynamic threshold gets the best performance in the simulations.