Problem solving during artificial selection of self-replicating loops

Emergence of self-replicating structures in a cellular automata space

In this paper we investigate the use of Artificial Immune Systems' principles to cope with the satisfiability problem. We describe ClonSAT, a new iterative approach for solving the well known Maximum Satisfiability (Max-SAT) problem. This latter has been shown to be NP-hard if the number of variables per clause is greater than 3. The underlying idea is to harness the optimization capabilities of artificial clonal selection algorithm to achieve good quality solutions for MaxSAT problem. To foster the process, a local search has been used. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed hybrid approach.

This dissertation is to illustrate the current state of the art of DNA computing achievements, especially of new approaches to solve theoretical 3-SAT problems and the hitting-set problem. Beginning with Adleman’s breakthrough which is an molecular algorithm for the solution of a NP-complete, combinatorial problem, the directed Hamiltonian path problem (HPP). Today, many researchers all over the world concentrate on proposing new methods to solve engineering or application problems with a DNA computing approach. Satisfiability problem is given a Boolean formula, and decide if a satisfying truth assignment exists. ( ) ( ) … ( ) ( ) is an example of Boolean formula. k-SAT problem means that each clause has exactly k literals. Not-All-Equal (NAE) 3-SAT problem and One-In-Three (1IN3) 3-SAT problem are both NP-complete problems. In this dissertation, we present molecular solutions to find all true assignments (3-SAT problem) and furthermore find Not-All-Equal (NAE) solutions and One-In-Three (1IN3) solutions in DNA-based Supercomputing. Hitting-set problem assume that there exists a collection C of subsets of a finite set S, and a positive integer K  |S|, and we need to know if there is a subset  S with | |  K such that contains at least one element of each subset in C. In other words, is the subset that intersects every subset in C and is called the hitting-set. In this dissertation, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, an algorithm is introduced to find the number of ones from 2n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of all the presented DNA-based algorithms is also discussed. We describe time complexity and volume complexity of three Algorithms, numbers of test tube used and the longest library strand in solution space of all three Algorithms. Finally, the simulated experiment is applied to verify correctness of the proposed DNA-based algorithm for solving the One-In-Three (1IN3) 3-SAT problem, and simulation of Not-All-Equal (NAE) 3-SAT problem is similar. Also, another simulated experiment is applied to our proposed DNA-based algorithm 6-2, in order to solve the well-known hitting-set problem. This research has been motivated by the benefit and the application of DNA computing and gives new methods to solve two 3-SAT problems and the hitting-set problem which are NP-complete.

Propositional Satisfiability (SAT) is a keystone in the history of computer science. SAT was the first problem shown to be NP-complete in 1971 by Stephen Cook. Having passed more than 40 years from then, SAT is now a lively research field where theory and practice have a natural intermixing. In this talk, we overview the use of SAT in practical domains, where SAT is thought in a broad sense, i.e. including SAT extensions such as Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO) and Quantified Boolean Formulas (QBF).

Propositional satisfiability (SAT) is a fundamental problem of immense practical importance. While SAT is NP-complete when clauses can contain 3 literals or more, the problem can be solved in linear time when the given formula contains only binary clauses (2SAT). Many complete search algorithms for SAT solving have taken advantage of 2SAT information that occurs in the statement of the problem in order to simplify the solving process, only one that we are aware of uses 2SAT information that arises in the process of the search, as clauses are simplified. There are a number of possibilities for making use of 2SAT information to improve the SAT solving process: maintaining 2SAT satisfiability during search, detecting unit consequences of the 2SAT clauses, and Krom subsumption using 2SAT clauses. In this paper we investigate the tradeoffs of increasing complex 2SAT handling versus the search space reduction and execution time. We give experimental results illustrating that the SAT solver resulting from the best tradeoff is competitive with state of the art Davis-Putnam methods, on hard problems involving a substantial 2SAT component.

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special cases of the constraint satisfaction problem (CSP), which is the problem of determining whether a set of constraints is satisfiable. In this paper we study the worst-case time complexity of NP-complete CSPs. Our main interest is in the CSP problem parameterized by a constraint language Gamma (CSP(Gamma)), and how the choice of Gamma affects the time complexity. It is believed that CSP(Gamma) is either tractable or NP-complete, and the algebraic CSP dichotomy conjecture gives a sharp delineation of these two classes based on algebraic properties of constraint languages. Under this conjecture and the ETH, we first rule out the existence of subexponential algorithms for finite domain NP-complete CSP(Gamma) problems. This result also extends to certain infinite-domain CSPs and structurally restricted CSP(Gamma) problems. We then begin a study of the complexity of NP-complete CSPs where one is allowed to arbitrarily restrict the values of individual variables, which is a very well-studied subclass of CSPs. For such CSPs with finite domain D, we identify a relation SD such that (1) CSP({SD}) is NP-complete and (2) if CSP(Gamma) over D is NP-complete and solvable in O(c^n) time, then CSP({SD}) is solvable in O(c^n) time, too. Hence, the time complexity of CSP({SD}) is a lower bound for all CSPs of this particular kind. We also prove that the complexity of CSP({SD}) is decreasing when |D| increases, unless the ETH is false. This implies, for instance, that for every c>1 there exists a finite-domain Gamma such that CSP(Gamma) is NP complete and solvable in O(c^n) time.

The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard. Its main application is for designing periodic timetables in public transportation. To this end, the passengers' paths are required as input data. This is a drawback since the final paths which are used by the passengers depend on the timetable to be designed. Including the passengers' routing in the PESP hence improves the quality of the resulting timetables. However, this makes PESP even harder. Formulating the PESP as satisfiability problem and using SAT solvers for its solution has been shown to be a highly promising approach. The goal of this paper is to exploit if SAT solvers can also be used for the problem of integrated timetabling and passenger routing. In our model of the integrated problem we distribute origin-destination (OD) pairs temporally through the network by using time-slices in order to make the resulting model more realistic. We present a formulation of this integrated problem as integer program which we are able to transform to a satisfiability problem. We tested the latter formulation within numerical experiments, which are performed on Germany's long-distance passenger railway network. The computation's analysis in which we compare the integrated approach with the traditional one with fixed passengers' weights, show promising results for future scientific investigations.

Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that turns this equation into true equality of strings. The computational complexity of this problem remains unknown, with the best lower and upper bounds being, respectively, NP and PSPACE. Recently, the novel technique of recompression was applied to this problem, simplifying the known proofs and lowering the space complexity to (nondeterministic) O(n log n). In this paper we show that satisfiability of word equations is in nondeterministic linear space, thus the language of satisfiable word equations is context-sensitive. We use the known recompression-based algorithm and additionally employ Huffman coding for letters. The proof, however, uses analysis of how the fragments of the equation depend on each other as well as a new strategy for nondeterministic choices of the algorithm, which uses several new ideas to limit the space occupied by the letters.

Quantum annealing device has shown a great potential in solving discrete problems that are theoretically and empirically hard. Boolean Satisfiability (SAT) problem, determining if there is an assignment of variables that satisfies a given Boolean function, is the first proven NP-complete problem widely used in various domains. Here, we present a novel mapping of the SAT problem to the quadratic unconstrained binary optimization problem (QUBO), and further develop a tool flow embedding the proposed QUBO to the architecture of the commercialized quantum computer D-Wave. By leveraging electronic design automation techniques including synthesis, placement and routing, this is not only the first work providing the detail flow that embeds the QUBO, but also a technique scalable for real world applications and some hard SAT problems with over 6000 variables in QUBO. Based on our results, we discuss the challenges in solving SAT using the current generation of annealing device, and explore the problem solving capability of future quantum annealing computers.

Numerous varieties of life forms have filled the earth throughout evolution. Evolution consists of two processes: self-replication and interaction with the physical environment and other living things around it. Initiated by von Neumann et al. studies on self-replication in cellular automata have attracted much attention, which aim to explore the logical mechanism underlying the replication of living things. In nature, competition is a common and spontaneous resource to drive self-replications, whereas most cellular-automaton-based models merely focus on some self-protection mechanisms that may deprive the rights of other artificial life (loops) to live. Especially, Huang et al. designed a self-adaptive, self-replicating model using a greedy selection mechanism, which can increase the ability of loops to survive through an occasionally abandoning part of their own structural information, for the sake of adapting to the restricted environment. Though this passive adaptation can improve diversity, it is always limited by the loop’s original structure and is unable to evolve or mutate new genes in a way that is consistent with the adaptive evolution of natural life. Furthermore, it is essential to implement more complex self-adaptive evolutionary mechanisms not at the cost of increasing the complexity of cellular automata. To this end, this article proposes new self-adaptive mechanisms, which can change the information of structural genes and actively adapt to the environment when the arm of a self-replicating loop encounters obstacles, thereby increasing the chance of replication. Meanwhile, our mechanisms can also actively add a proper orientation to the current construction arm for the sake of breaking through the deadlock situation. Our new mechanisms enable active self-adaptations in comparison with the passive mechanism in the work of Huang et al. which is achieved by including a few rules without increasing the number of cell states as compared to the latter. Experiments demonstrate that this active self-adaptability can bring more diversity than the previous mechanism, whereby it may facilitate the emergence of various levels in self-replicating structures.

The partial string avoidability problem, also known as partial word avoidability, is stated as follows: given a finite set of strings with possible ``holes'' (undefined symbols), determine whether there exists any two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this paper establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form (CNF) satisfiability problem (SAT), with each clause having infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting constraints (such as clauses, inequalities, polynomials, etc). Two results on their proof complexity are established. First, there is a particular formula that has a short refutation in Resolution with shift, but requires classical proofs of exponential size (Resolution, Cutting Plane, Polynomial Calculus, etc.). At the same time, exponential lower bounds for shifted versions of classical proof systems are established.

In this paper, we present a Satisfiability Modulo Theory based (SMT-based) bounded model checking (BMC) method for Timed Real-Weighted Interpreted Systems and for the existential fragment of the Weighted Epistemic Computation Tree Logic. SMT-based bounded model checking consists in translating the existential model checking problem for a modal logic and for a model to the satisfiability problem of a quantifier-free first-order formula. We have implemented the SMT-BMC method and performed the BMC algorithm on Timed Weighted Generic Pipeline Paradigm benchmark. The preliminary experimental results demonstrate the feasibility of the method. To perform the experiments, we used the state of the art SMT-solver Z3.

While a number of weak consistency mechanisms have been developed in recent years to improve performance and ensure availability in distributed, replicated systems, ensuring the correctness of transactional applications running on top of such systems remains a difficult and important problem. Serializability is a well-understood correctness criterion for transactional programs; understanding whether applications are serializable when executed in a weakly-consistent environment, however remains a challenging exercise. In this work, we combine a dependency graph-based characterization of serializability and leverage the framework of abstract executions to develop a fully-automated approach for statically finding bounded serializability violations under any weak consistency model. We reduce the problem of serializability to satisfiability of a formula in First-Order Logic (FOL), which allows us to harness the power of existing SMT solvers. We provide rules to automatically construct the FOL encoding from programs written in SQL (allowing loops and conditionals) and express consistency specifications as FOL formula. In addition to detecting bounded serializability violations, we also provide two orthogonal schemes to reason about unbounded executions by providing sufficient conditions (again, in the form of FOL formulae) whose satisfiability implies the absence of anomalies in any arbitrary execution. We have applied the proposed technique on TPC-C, a real-world database program with complex application logic, and were able to discover anomalies under Parallel Snapshot Isolation (PSI), and verify serializability for unbounded executions under Snapshot Isolation (SI), two consistency mechanisms substantially weaker than serializability.

The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often ...

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential quantifiers that leave at most one variable free. We investigate one-dimensional fragment over words and over omega-words. We show that it is expressively equivalent to the two-variable fragment of first-order logic. We also show that its satisfiability problem is NExpTime-complete. Further, we show undecidability of some extensions, whose two-variable counterparts remain decidable.