We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a given category with an involution. This syntax can be used to represent and reason about quantum processes.

The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems. Here we extend that work to a sound (but not necessarily complete) logic for composite systems, which brings together ideas from the quantum logic tradition with concepts from (dynamic) modal logic and from quantum computation. This Logic of Quantum Programs (LQP) is capable of expressing important features of quantum measurements and unitary evolutions of multi-partite states, as well as giving logical characterisations to various forms of entanglement (for example, the Bell states, the GHZ states etc.). We present a finitary syntax, a relational semantics and a sound proof system for this logic. As applications, we use our system to give formal correctness proofs for the Teleportation protocol and for a standard Quantum Secret Sharing protocol; a whole range of other quantum circuits and programs, including other well-known protocols (for example, superdense coding, entanglement swapping, logic-gate teleportation etc.), can be similarly verified using our logic.

This paper presents studies of the coordination of human upper body voluntary movement. A minimum-jerk 3D model is used to obtain the desired path in Cartesian space, which is widely used in the prediction of human reach movement. Instead of inverse kinematics, a direct optimization approach is used to predict each joint's profile (a spline curve). This optimization problem has four cost function terms: (1) Joint displacement function that evaluates displacement of each joint away from its neutral position; (2) Inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial target point to the final target point; (3) The non-smoothness function of the trajectory, which is the second derivative of the joint trajectory; (4) The non-continuity function, which consists of the amplitudes of joint angle rates at the initial and final target points, in order to emphasize smooth starting and ending conditions. This direct optimization technique can be used for potentially any number of degrees of freedom (DOF) system and it reduces the cost associated with certain inverse kinematics approaches for resolving joint profiles. This paper presents a high redundant upper-body modeling with 15 DOFs. Illustrative examples are presented and an interface is set up to visualize the results.

In our recent work, we have proposed a novel force control actuator system called series damper actuator (SDA). We have since built an SDA system based on magneto-rheological fluid (MR) damper. In this paper, the dynamics property of SDA system based on the MR fluid damper (SMRDA) is investigated. The effect of the extra dynamics introduced by the MR fluid damper is revealed by comparing the SMRDA with the SDA system based on a linear Newtonian viscous damper (SNVDA). To linearize the constitutive property of the MR fluid damper, a modified Bingham model is proposed. A force feedback control loop is implemented after the linearization. An experimental SMRDA is built to illustrate the performance of the SDA system.

We divide infinite sequences of subword complexity 2n+1 intofour subclasses with respect to left and right special elementsand examine the structure of the subclasses with the help of Rauzygraphs. Let k ≥ 2 be an integer. If the expansion in base kof a number is an Arnoux-Rauzy word, then it belongs to Subclass Iand the number is known to be transcendental. We prove thetranscendence of numbers with expansions in the subclasses II andIII.

This Special Issue of RAIRO, Theoretical Informatics and Applicationsis devoted to full versions of selected papers from the workshop WordAvoidability, Complexity and Morphisms which took place in Turku(Finland) on July 2004, as a satellite event of the conferenceICALP'2004.
The topics of this one day workshop concern particular aspects ofCombinatorics on Words: string pattern avoidability, complexities offinite or infinite words, and free monoids morphims.
The scientificprogram of the worshop consisted of two invited lectures given byA.E. Frid and J. Shallit as well as presentations of 8 contributedpapers selected by the Program Committee from a total of 12submissions.
The Program Committee consisted of :A. Carpi (Perugia),J. Cassaigne (Marseille),J. Currie (Winnipeg), I. Petre (Turku),G. Richomme (Amiens),A. M. Shur (Ekaterinburg), andP. Séébold (Montpellier). 
This special issue contains the full text of five of the paperspresented at the workshop. All of them were normally refereed andrevised.
I would like to thank everybody who contributed to the workshop andthis issue including invited speakers, members of the programCommittee, ICALP'2004's organization, authors and all referees of paperssubmitted to the worshop and this special issue. I am indebtful toJ. Kärhumaki and J. Berstel for thinking of me to organize thisworkshop. Special thanks to P. Séébold for all his advices. Finally Iam grateful to C. Choffrut, the editor-chief of the RAIRO-TIA foraccepting to publish this special issue.

We present an algorithm which produces, in some cases, infinite wordsavoiding both large fractional repetitions and a given set of finite words.We use this method to show that all the ternary patterns whose avoidabilityindex was left open in Cassaigne's thesis are 2-avoidable.We also prove that there exist exponentially many $\frac{7}{4}^+$ -free ternary wordsand $\frac{7}{5}^+$ -free 4-ary words.Finally we give small morphisms for binary words containing only the squares 2,12 and (01)² and for binary words avoiding large squares and fractional repetitions.

Let I be a finite set of words and $\Rightarrow_I^*$ be the derivation relationgenerated by the set of productions {ε → u | u ∈ I}.Let $L_I^{\epsilon}$ be the set of words u such that $\epsilon\Rightarrow_I^* u$ .We prove that the set I is unavoidable if and only if the relation $\Rightarrow_I^*$ is a well quasi-order on the set $L_I^{\epsilon}$ . This result generalizes a theorem of[Ehrenfeucht et al., Theor. Comput. Sci.27 (1983) 311–332]. Further generalizations are investigated.

We investigate the complexity of several problems concerning Las Vegas finite automata. Our results are as follows. (1) The membership problem for Las Vegas finite automata is in NL. (2) The nonemptiness and inequivalence problems for Las Vegas finite automata are NL-complete. (3) Constructing for a given Las Vegas finite automaton a minimum state deterministic finite automaton is in NP. These results provide partial answers to some open problems posed by Hromkovič and Schnitger [Theoret. Comput. Sci.262 (2001)1–24)].

We consider the position and number of occurrences of squaresin the Thue-Morse sequence, and show that the corresponding sequencesare 2-regular. We also prove that changing any finite but nonzeronumber of bits in the Thue-Morse sequence creates an overlap, and anylinear subsequence of the Thue-Morse sequence (except those correspondingto decimation by a power of 2) contains an overlap.

The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length n which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length n. In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely, for each sequence u of subword complexity ƒu(n) and for each prime p ≥ 3 we build a Toeplitz word on the same alphabet whose arithmetical complexity is $a(n)=\Theta(n f_u(\lceil \log_p n \rceil))$ .

The paper treats the question whether there always exists a minimal nondeterministic finite automaton of n states whose equivalent minimal deterministic finite automaton has α states for any integers n and α with n ≤ α ≤ 2n .Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003). In the present paper, the question is completely solved by presenting appropriate automata for all values of n and α. However, in order to give an explicit construction of the automata, we increase the input alphabet to exponential sizes. Then we prove that 2n letters would be sufficient but we describe the related automata only implicitly. In the last section, we investigate the above question for automata over binary and unary alphabets.

Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic,then it can be extended by the left with one or two lettersin such a way that it remains morphic and Sturmian.Yasutomi (1997) has proved that these were the sole possible additions andthat, if we cut the first letters of such a word, it didn't remain morphic.In this paper, we give an elementary and combinatorial proof of this result.