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134
Four Small Universal Turing Machines
, 2009
"... We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machin ..."
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Cited by 21 (7 self)
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We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. Also, all of the universal machines we present here simulate Turing machines in polynomial time.
DNA Computing Based on Splicing: The Existence of Universal Computers
 THEORY OF COMPUTING SYSTEMS
, 1995
"... Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is ..."
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Cited by 21 (3 self)
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Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is added. We also show that there exist universal splicing systems with the properties above, i. e. there exists a universal splicing system with fixed components which can simulate the behaviour of any given splicing system, when an encoding of the particular splicing system is added to its set of axioms. In this way the possibility of designing programmable DNA computers based on the splicing operation is proved.
Reachability in Succinct and Parametric OneCounter Automata
"... Abstract. Onecounter automata are a fundamental and widelystudied class of infinitestate systems. In this paper we consider onecounter automata with counter updates encoded in binary—which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of mac ..."
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Cited by 18 (7 self)
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Abstract. Onecounter automata are a fundamental and widelystudied class of infinitestate systems. In this paper we consider onecounter automata with counter updates encoded in binary—which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of machines is in PSpace and is NPhard. One of the main results of this paper is to show that this problem is in fact in NP, and is thus NPcomplete. We also consider parametric onecounter automata, in which counter updates be integervalued parameters. The reachability problem asks whether there are values for the parameters such that a final state can be reached from an initial state. Our second main result shows decidability of the reachability problem for parametric onecounter automata by reduction to existential Presburger arithmetic with divisibility. 1
The Undecidability of Second Order Multiplicative Linear Logic
, 1996
"... The multiplicative fragment of second order propositional linear logic is shown to be undecidable. Introduction Decision problems for propositional (quantifierfree) linear logic were first studied by Lincoln et al. [LMSS]. In referring to linear logic fragments, let M stand for multiplicatives, A ..."
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Cited by 14 (3 self)
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The multiplicative fragment of second order propositional linear logic is shown to be undecidable. Introduction Decision problems for propositional (quantifierfree) linear logic were first studied by Lincoln et al. [LMSS]. In referring to linear logic fragments, let M stand for multiplicatives, A for additives, E for exponentials (or modalities), 1 for first order quantifiers, 2 for second order propositional quantifiers, and I for "intuitionistic" version. In [LMSS] it was shown that full propositional linear logic is undecidable and that MALL is PSPACEcomplete. The main problems left open in [LMSS] were the NPcompleteness of MLL, the decidability of MELL, and the decidability of various fragments of propositional linear logic without exponentials but extended with second order propositional quantifiers. The decision problem for MELL is still open, but almost all the other problems have been solved: ffl The NPcompleteness of MLL has been obtained by Kanovich [K1]. Moreover, Linco...
Typability and Type Checking in the SecondOrder lambdaCalculus Are Equivalent and Undecidable
, 1993
"... We consider the problems of typability and type checking in the Girard/Reynolds secondorder polymorphic typedcalculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pureterms. These problems have been considere ..."
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Cited by 13 (1 self)
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We consider the problems of typability and type checking in the Girard/Reynolds secondorder polymorphic typedcalculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pureterms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lowerbound complexity results for System F have been achieved, but they have remained "embarrassing open problems" 3 for System F itself. We first prove that type checking in System F is undecidable by a reduction from semiunification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructingterms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specif subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment maybe simulated. We develop this method, which we call \constants for free", for both the K and I calculi.
Counter Machines and Verification Problems
"... We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, inniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and parameterized ..."
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Cited by 13 (2 self)
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We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, inniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and parameterized constants (e.g., \Is 3x 5y 2D 1 +9D 2 < 12?", where x; y are counters, and D 1 ; D 2 are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the verication /debugging of safety properties in innitestate transition systems. For example, we show that (binary, forward, and backward) reachability and safety are solvable for these machines. Key words: Counter machines, automated verication, innitestate systems, reachability 1 A short version [15] of this paper appeared in the Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science (MFCS 2000), Lecture Notes in Computer Science 1893 (Springer, Berlin, 2000) 426435. 2 The work by Oscar H. Ibarra and Jianwen Su has been supported in part by NSF grants IRI9700370 and IIS9817432. 3 The work by Zhe Dang and Richard A. Kemmerer has been supported in part by the Defense Advanced Research Projects Agency (DARPA) and Rome Laboratory, Air Force Material Command, USAF, under agreement number F306029710207. 4 The work by Tevk Bultan has been supported in part by NSF grant CCR9970976 and NSF CAREER award CCR9984822. Preprint submitted to Elsevier Science 17 April 2001 1
The Undecidability Of Second Order Linear Logic Without Exponentials
 Journal of Symbolic Logic
, 1995
"... . Recently, Lincoln, Scedrov and Shankar showed that the multiplicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicativeadditive fragment, but it does not work in the classical c ..."
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Cited by 12 (3 self)
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. Recently, Lincoln, Scedrov and Shankar showed that the multiplicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicativeadditive fragment, but it does not work in the classical case, because second order classical logic is decidable. Here we show that the multiplicativeadditive fragment of second order classical linear logic is also undecidable, using an encoding of twocounter machines originally due to Kanovich. The faithfulness of this encoding is proved by means of the phase semantics. In this paper, we write LL for the full propositional fragment of linear logic, MLL for the multiplicative fragment, MALL for the multiplicativeadditive fragment, and MELL for the multiplicativeexponential fragment. Similarly, we write ILL, IMLL, etc. for the fragments of intuitionistic linear logic, LL2, MLL2, etc. for the second order fragments of linear logic, and ILL2, IML...
Composability of infinitestate activity automata
, 2004
"... Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accep ..."
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Cited by 12 (3 self)
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Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accepted by. For a nonnegative integer, alookahead delegator for is a deterministic machine in which, knowing (a) the current states! of and the accessible “local ” information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the lookahead symbols to the right of the current input symbol being processed, can uniquely determine " the to assign the current symbol. Moreover, every string accepted by is also accepted by, i.e., the subsequence of string delegated by to " each is accepted by. Thus,lookahead delegation is a stronger requirement than composability, since the delegator must be deterministic. A system that is composable may not have adelegator for any. We look at the decidability of composability and existence ofdelegators for various classes of machines. Our results have applications to automated composition of eservices. E
On P systems operating in sequential mode
 International Journal of Foundations of Computer Science
, 2004
"... 1. For 1membrane catalytic systems (CS's), the sequential version is strictlyweaker than the parallel version in that the former defines (i.e. generates) exactly the semilinear sets, whereas the latter is known to define nonrecursivesets. 2. For 1membrane communicating P systems (CPS's), ..."
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1. For 1membrane catalytic systems (CS's), the sequential version is strictlyweaker than the parallel version in that the former defines (i.e. generates) exactly the semilinear sets, whereas the latter is known to define nonrecursivesets. 2. For 1membrane communicating P systems (CPS's), the sequential versioncan only define a proper subclass of the semilinear sets, whereas the parallel version is known to define nonrecursive sets.3. Adding a new type of rule of the form: ab! axbyccomedcome to the CPS(a natural generalization of the rule ab! axbyccome in the original model),where x; y 2 fhere; outg, to the sequential 1membrane CPS makes itequivalent to a vector addition system.