Work Tape Research Articles

Uncountable Realtime Probabilistic Classes

We investigate the minimal cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On non-unary case, we obtain the same result for double logarithmic space, which is also tight. When replacing the work tape with a few counters, we can still achieve similar results for unary linear-space two-counter automata, unary sublinear-space three-counter automata, and non-unary sublinear-space two-counter automata. We also show how to slightly improve the sublinear-space constructions by using more counters.

Deterministic One-Way Turing Machines with Sublinear Space

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.

Wear Analysis of Warm Extrusion Dies Using DEFORM

Based on a modified form of Archard’s wear theory, significant data were obtained using the finite element analysis code DEFORM during the process of warm extrusion, including instantaneous interface temperature, sliding velocity, and interface pressure distribution of every node. From the acquired data, the wear of the punch, the temperature–wear coefficient curve, temperature–wear depth curve, and temperature–hardness curve were acquired. The results show that the maximum wear occurred in the front working tape of the punch. The results are in agreement with actual conditions, and therefore, lay a foundation for forecasting die life and optimizing die cavity profiles using this method.

Automatic functions, linear time and learning

The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time notions permit full learnability for learning in the limit of automatic classes (families of languages which are uniformly recognised by a finite automaton). In particular it is shown that a function is automatic iff there is a one-tape Turing machine with a left end which computes the function in linear time where the input before the computation and the output after the computation both start at the left end. It is known that learners realised as automatic update functions are restrictive for learning. In the present work it is shown that one can overcome the problem by providing work tapes additional to a resource-bounded base tape while keeping the update-time to be linear in the length of the largest datum seen so far. In this model, one additional such work tape provides additional learning power over the automatic learner model and two additional work tapes give full learning power. Furthermore, one can also consider additional queues or additional stacks in place of additional work tapes and for these devices, one queue or two stacks are sufficient for full learning power while one stack is insufficient.

And God Created Great Whales by Rinde Eckert (review)

Reviewed by: And God Created Great Whales by Rinde Eckert Jonathan Chambers And God Created Great Whales. By Rinde Eckert. Directed by David Schweizer. Culture Project in Association with Elisha Wiesel, Culture Project, New York City. 29 February 2012. From the 1920s to the ’40s American literary scholars gradually reclaimed Moby-Dick from the edges of oblivion. Mostly forgotten by all but the most erudite, the novel, first published in 1851 to lukewarm critical and popular response, was initially rediscovered by Carl Van Doren and D. H. Lawrence in the early 1920s, and subsequently lauded by many notable literary critics as the consummate American novel. By mid-century, Moby-Dick had been fashioned into Melville’s magnum opus, and its characters—principally Ahab and Ishmael—had become iconic, representing the best (that is, adventurous individualism) and worst (obsessive hubris) facets of the American spirit. Given its profound cultural cache, it is not surprising that Melville’s novel has inspired myriad artists following in its wake. The diversity of adaptations is impressive, ranging from the avant-garde (for example, Laurie Anderson’s Songs and Stories from Moby-Dick) to the popular (the “Möbius Dick” episode of Futurama). Although the motivations driving these and other Moby-Dick-inspired reflections, reimaginings, and borrowings are as varied as the works themselves, their very existence validates the point that Melville’s most famous work remains a powerful referent for American artists seeking to understand themselves and their universe. Within this tradition of Moby-Dick inspiration is Rinde Eckert’s new music-theatre piece And God Created Great Whales. Created, written, and composed by Eckert (who also performs), with direction by David Schweizer, And God Created Great Whales was originally developed at P.S.122 in the late 1990s. Later staged at the Foundry Theatre and the Culture Project in 2000 and 2001, the production has periodically been remounted nationally and internationally. The 2012 revival, again directed by Schweizer, was essentially a faithful restaging of the original version. In it, Eckert ruminated on a number of weighty themes, including the vexed process of artistic creation, the burden of obsession, the convolution of consciousness and memory, and the specter of death. As with Eckert’s other pieces that draw upon extant texts, And God Created Great Whales’ relation to its source material is more thematic than literal. Nathan, played by Eckert, is a piano-tuner and composer who hopes to finish an opera based on Melville’s masterpiece before his memory fails. Nathan’s disintegrating consciousness is an analogue for the physical challenges Melville’s Ahab faces in his obsessive pursuit of Moby-Dick. To compensate for his failing memory, Nathan relies on a collection of color-coded tape recorders marked for specific purposes—blue is the “master tape,” green is for “incidental notes,” red is the “working tape,” and so on—and he also wears a tape recorder hung around his neck. Although the voice on the tapes is that of Nathan, recorded at a time when he was still lucid and aware of his condition, it is not clear how this system of recording was created, what caused his condition in the first place, how long it has been going on, or how much time passes during the action of the performance. Eckert’s refusal to provide answers to these questions invests the time, place, and action of And God Created Great Whales with a sense of swirl and blur. The revival production emphasized this sensation. Most notably, Eckert and Schweizer sought less a real-world/physical locale and instead set the action in the realm of Nathan’s consciousness. While the setting was, in a literal sense, Nathan’s apartment/studio, it was also something more. Designed by John Torres and Caleb Wertenbaker (based on original designs by Kevin Abrams), a baby-grand piano, wrapped with sailing line that evoked the rigging of Melville’s whaleboat, the Pequod, dominated the stage. Two ends of the sailing line extended vertically into a triangle suggesting a sail. Surrounding the piano-boat were bits of scrap paper, flash cards, items torn from magazines and books, and cassette tapes. The purpose of these items was ambiguous. Were...

Tradeoff lower lounds for stack machines

A space-bounded Stack Machine is a regular Turing Machine with a read-only input tape, several space-bounded read-write work tapes, and an unbounded stack. Stack Machines with a logarithmic space bound have been connected to other classical models of computation, such as polynomial-time Turing Machines (P) (Cook in J Assoc Comput Mach 18:4---18, 1971) and polynomial size, polylogarithmic depth, bounded fan-in circuits (NC) e.g., Borodin et al. (SIAM J Comput 18, 1989). In this paper, we present significant new lower bounds and techniques for Stack Machines. This comes in the form of a trade-off lower bound between space and number of passes over the input tape. Specifically, we give an explicit permuted inner product function such that any Stack Machine computing this function requires either $${\Omega (N^{1/4 - \epsilon})}$$ space or $${\Omega (N^{1/4 - \epsilon})}$$ number of passes for every constant $${\epsilon > 0}$$ , where N is the input size. In the case of logarithmic space Stack Machines, this yields an unconditional $${\Omega (N^{1/4 - \epsilon})}$$ lower bound for the number of passes. To put this result in perspective, we note that Stack Machines with logarithmic space and a single pass over the input can compute Parity, Majority, as well as certain languages outside NC. The latter follows from Allender (J Assoc Comput Mach 36:912---928, 1989), conditional on the widely believed complexity assumption that PSPACE $${\subsetneq}$$ EXP. Our technique is a novel communication complexity reduction, thereby extending the already wide range of models of computation for which communication complexity can be used to obtain lower bounds. Informally, we show that a k-player number-in-hand (NIH) communication protocol for a base function f can efficiently simulate a space- and pass-bounded Stack Machine for a related function F, which consists of several "permuted" instances of f, bundled together by a combining function h. Trade-off lower bounds for Stack Machines then follow from known communication complexity lower bounds. The framework for this reduction was given by Beame & Huynh-Ngoc (2008), who used it to obtain similar trade-off lower bounds for Turing Machines with a constant number of pass-bounded external tapes. We also prove that the latter cannot efficiently simulate Stack Machines, conditional on the complexity assumption that E $${\not \subset}$$ PSPACE. It is the treatment of an unbounded stack which constitutes the main technical novelty in our communication complexity reduction.

Mechanical and corrosion performance of SiC multilayer containing porous layers

Presently, one of the most interesting approaches to the generation of H2 is based on sulphur-based cycles, that however require structural components able to work in a corrosive environment at high temperature. Silicon carbide (SiC) is one of the most promising materials for this application, and to increase its limited toughness multilayered structures can be envisaged, since crack deviation and delamination increase energy adsorption during fracture. In this work tape casting and pressureless sintering were used to produce SiC samples consisting in alternating dense and porous layers, the porosity being realised by the insertion of pore forming agents during the preparation of the green ceramic. The mechanical properties of these materials were studied both at room temperature and at 1550 °C. The effect of corrosion at 850 °C by a mixture of H2O, O2 and SO2 was studied by comparing microstructure and mechanical behaviour before and after long-term (1000 h) corrosion treatments. Corrosion resistance was very good, and flexural strength was strongly increased due to a combined effect of crack tip blunting and compressive residual stress formation. Concerning the architecture instead, the insertion of porous layers brings to a reduction of flexural strength, while Young's modulus remains almost constant.

On Approximate Majority and Probabilistic Time

We prove new results on the circuit complexity of approximate majority, which is the problem of computing the majority of a given bit string whose fraction of 1’s is bounded away from 1/2 (by a constant). We then apply these results to obtain new relationships between probabilistic time, BPTime (t), and alternating time, ∑O(1)Time (t). Our main results are the following: We prove that depth-3 circuits with bottom fan-in (log n)/2 that compute approximate majority on n bits must have size at least $$2^{n^{0.1}}$$. As a corollary we obtain that there is no black-box proof that BPTime (t) $$\subseteq \sum_2$$Time (o(t2)). This complements the (black-box) result that BPTime (t) $$\subseteq \sum_2$$Time (t2 · poly log t) (Sipser and Gacs, STOC ’83; Lautemann, IPL ’83). We prove that approximate majority is computable by uniform polynomial-size circuits of depth 3. Prior to our work, the only known polynomial-size depth-3 circuits for approximate majority were non-uniform (Ajtai, Ann. Pure Appl. Logic ’83). We also prove that BPTime (t) $$\subseteq \sum_3$$Time (t · poly log t). This complements our results in (1). We prove new lower bounds for solving QSAT3 $$\in \sum_3$$Time (n · poly log n) on probabilistic computational models. In particular, we prove that solving QSAT3 requires time n1+Ω(1) on Turing machines with a random-access input tape and a sequential-access work tape that is initialized with random bits. No nontrivial lower bound was previously known on this model (for a function computable in linear space).

Traces of term-automatic graphs

In formal language theory, many families of languages are defined using either grammars or finite acceptors. For instance, context-sensitive languages are the languages generated by growing grammars, or equivalently those accepted by Turing machines whose work tape's size is proportional to that of their input. A few years ago, a new characterisation of context-sensitive languages as the sets of traces, or path labels, of rational graphs (infinite graphs defined by sets of finite-state transducers) was established. We investigate a similar characterisation in the more general framework of graphs defined by term transducers. In particular, we show that the languages of term-automatic graphs between regular sets of vertices coincide with the languages accepted by alternating linearly bounded Turing machines. As a technical tool, we also introduce an arborescent variant of tiling systems, which provides yet another characterisation of these languages.

A time lower bound for satisfiability

We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time n a for a < ( d + 2 ) / ( d + 1 ) . For conondeterministic machines, we obtain a similar lower bound for any a such that a 3 < 1 + a / ( d + 1 ) . The same bounds apply to almost all natural NP -complete problems known.

A variant of inductive counting

We present a new version of the inductive counting, accepting the complement of an NSPACE(s(n)) language nondeterministically in space O(s(n)) , independent of whether s(n)⩾ log n , but using an additional “one-way pebble” – a movable marker placed on the input tape. This reduces the space used by inductive counting to log n+ O(s(n)) bits on the binary work tape and gives the weakest known nondeterministic device accepting a co− NSPACE( o( log n)) language.

Parallel RAMs with owned global memory and deterministic context-free language recognition

We identify and study a natural and frequently occurring subclass of Concurrent Read, Exclusive Write Parallel Random Access Machines (CREW-PRAMs). Called Concurrent Read, Owner Write, or CROW-PRAMS, these are machines in which each global memory location is assigned a unique “owner” processor, which is the only processor allowed to write into it. Considering the difficulties that would be involved in physically realizinga full CREW-PRAM model and demonstrate its stability under several definitional changes. Second, we precisely characterize the power of the CROW-PRAM by showing that the class of languages recognizable by it in time O (log n) (and implicity with a polynomial number of processors) is exactly the class LOGDCFL of languages log space reducible to deterministic context-free languages. Third, using the same basic machinery, we show that the recognition problem for deterministic context-free languages can be solved quickly on a deterministic auxilliary pushdown automation having random access to its input tape, a log n space work tape, and pushdown store of small maximum height. For example, time O ( n 1 + ε ) is achievable with pushdown height O (log 2 n ). These result extend and unify work of von Braunmöhl, Cook, Mehlhorn, and Verbeek, Klein and Reif; and Rytter.

Matching upper and lower bounds for simulations of several linear tapes on one multidimensional tape

We prove an O(t(n) d (t(n)) ½ / log t(n)) time bound for the sim-ulation of t(n) steps of a Turing machine using several one-dimensional work tapes on a Turing machine using one d-dimensional work tape, $ d \ge 2 $ . We prove a matching lower bound which holds for the problem of recognizing languages on machines with a separate one-way input tape.

Computational complexity of functions

Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [9] (see also [6]). Earlier relevant work (classical theorems like Compression, Speed-up, etc.) was done in [15,13,2,1,14,7]. I translated only the part with the statement of the results. Instead of the proof part, I appended a later (1979, unpublished) proof sketch of a slightly tighter version. The improvement is based on the results of Meyer and Winklmann [8] and Sipser [12]. Meyer and Winklmann extended earlier versions to machines with a separate input and working tape, thus allowing complexities smaller than the input length (down to its log). Sipser showed the space-bounded Halting Problem to require only additive constant overhead. The proof in the appendix below employs both advances to extend the original proofs to machines with a fixed alphabet and a separate input and working space. The extension has no (even logarithmic) restrictions on complexity and no overhead (beyond an additive constant). The sketch is very brief and a more detailed exposition is expected later [11].

THE EFFECT OF INKDOTS FOR TWO-DIMENSIONAL AUTOMATA

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

Two tapes versus one for off-line Turing machines

We prove the first superlinear lower bound for a concrete, polynomial time recognizable decision problem on a Taring machine with one work tape and a two-way input tape (also called off-line 1-tape Turing machine). In particular, for offline Turing machines we show that two tapes are better than one and that three pushdown stores are better than two (both in the deterministic and in the nondeterministic case).

The speed of copying on one-tape off-line Turing machines

It is shown that one-tape off-line Turing machines (TMs), i.e., Turing machines with one work tape and a two-way input tape, can copy a string of length s across d cells on the work tape in O(d+ sd log(min{n,d})) steps, where n denotes the length of the input. This observation is used to show that such TMs can simulate f( n)-time bounded multi-tape TMs in O( f(n) 2 log(n)) steps. This is faster by a factor of log n than the straightforward simulations. Further it is shown (by a Kolmogorov complexity argument) that often this upper bound for copying is optimal: one-tape off-line TMs need ω( sd log(min{n,d})) steps for copying a string of lenght s across d cells, if d⩾ s⩾ log n.

A note on nondeterminism in small, fast parallel computers

Nondeterministic analogues of the well-known language classes NC and SC called NNC and NSC, respectively, are investigated. NC is the class of languages that can be accepted by small, fast parallel computers; SC is the class of languages that can be recognized by a deterministic Turing machine in polynomial time and polylog tape-head reversals. Adding nondeterminism to SC leaves it in the domain of parallel computation since NSC contained in POLYLOGSPACE. That is, NSC is a subset of the class of languages computable by fast parallel computers. Adding nondeterminism to NC appears to make it much more powerful since NNC=NP. It is clear that NSC contained in NNC, and probable that NSC contained in/implied by NNC. Further evidence for this conjecture is provided by showing that NSC is precisely the class of languages recognizable in simultaneous polynomial time and polylog reversals by a nondeterministic Turing machine with a read-only input tape and a single read-write work tape; it is known that NNC is similar, but is recognizable by a Turing machine with two read-write tapes. >

Alternating real-time computations

The effect of the number of work tapes on computational power of real-time Turing machines is considered. Well-known results state that k tapes are better than k–1 tapes in the case of deterministic machines and, for nondeterministic ones, two tapes are as good as many tapes. We show that alternating real-time pushdown automata recognize the same class of languages as multitape alternating machines working in linear time. It is also shown that the automata making a constant number of alternations and only one reversal recognize exactly rudimentary languages.

Speed-Up of Turing Machines with One Work Tape and a Two-Way Input Tape

In this paper we consider the next more powerful restricted type of Turing machine, which cannot be handled by the existing lower bound arguments: Turing machines with one work tape and a two-way input tape. We show that one can simulate a deterministic Turing machine of this type with time bound $O(n^3 )$ by $\Sigma _2 $-Turing machine of the same type with time bound $O(n^2 \cdot \log ^2 n)$. This implies the new separation result $\Sigma _2 {\operatorname{TIME}}_1 (n) \nsubseteq {\operatorname{DTIME}}_1 ({{n^{{3 / 2}} } / {\log ^6 n}})$. Further, we improve Kannan’s separation result ${\operatorname{NTIME}}(n) \nsubseteq {\operatorname{DTIME}}_1 (n^{1.104} )$ to ${\operatorname{NTIME}}(n) \nsubseteq {\operatorname{DTIME}}_1 (n^{1.22} )$. Finally we show that with Turing machines of the considered type that use $2k$ alternations, the achieved speed-up increases and for large k approximates $t^{{1 / 2}} (n)$. In view of the close relationship between spacebounded Turing machines and time-bounded Turing m...